What if the English protectorate had established a more permanent constitutional settlement? The most likely way for this to happen would be if the "Instrument of government" drafted by Major General John Lambert was modified further before being adopted in 1653.  Perhaps if General Henry Ireton had not died of a fever in Ireland in 1651, he would have been around to do this.  Ireton had been involved in the previous "Agreement of the people"; was generally a bit more radical than some of the other officers and more attuned to the desires of the common soldiers.  As Oliver Cromwell’s son in law, he had influence.  So point of departure is in 1651 or 1653.

Suppose the " Instrument" had proposed not just a two pole system of protector and parliament, but a three pole system adding another house of parliament, elected not by those with property, but by the Army (and the Navy, unified at the time).  Let’s call it the House of Martials.  This fits with the desire of Cromwell for a balance neither absolute monarchy nor absolute rule by parliament, both of which seemed to have failed at this point.  It also balances the tension between civilian parliamentarians and the army.  House of Martials would have veto over defence.  House of Commons would have veto over taxes.  Both houses can propose legislation, but needs to be ratified either by other house or by the protector.  Protector proposes council of state to act as executive cabinet, but needs to be ratified both houses of parliament.

House of Martials elected mostly on regimental basis.  Generals each appoint one seat, possibly themselves.  Junior officers elect two seats between them, enlisted men also elect two seats.  Honourably disbanded veterans form a territorial resrve, and also elect some seats.

Elections and reratifications every three years, except for the protector who rules for life unless he chooses to retire.
Protector has to nominate one of the Council of State as temporary successor in event of his death or retirement, but only both houses of parliament together can choose the next protector when the time comes. This nominated successor position will ultimate evolve into a prime minister-like role.

All parliamentarians, councillors of state and the protector need to swear oath to uphold "Instrument of government" as condition of taking office.  Opponents are either excluded altogether (royalists for at least 9 years), or co-opted into the system (republican parliamentarians like Hesilrige or levelers like Lilburne).

So what else changes as a result?

With no restoration, there would not be a second Anglo-Dutch war.  Although trade rivalry would maintain tensions, without Charles II's push for his nephew William to become stadtholder there is no immediate causus belli. Perhaps a later war as trade tensions increase (Dutch outcompeting English shipping), but not then (co-protestant views in House of Martials have veto over mercantile views in House of Commons.)  So no seizure of New Netherlands in America.

English maintain continental foothold in Dunkirk (not sold to France as by Charles II in OTL).
Hence more interest in containing French expansion in Spanish Netherlands (though not averse to taking more themselves). Hence would be likely to still join triple alliance with Dutch and Swedes.  Would not join France in attacking Dutch in 1672, but would probably stay neutral and not aid Dutch either (as attack through Munster and Cologne not Spanish Netherlands).  This, together with William III becoming stadtholder as a result of French invasion, worsens Anglo-Dutch relations.
So potentially another Anglo-Dutch war later in 1670s or early 1680s. Not sure what trigger would be. Certainly William would be interested in doing something like the glorious revolution if he thought he could pull it off (unlikely - potentially he tries to put Charles II on throne, but more likely he presents himself as protestant saviour if English regime has a shaky transition (first civilian protector??)).  English army would win on home ground in this scenario.
Alternatively English join with Louis XIV of France and attack Dutch, possibly also attacking Spanish Netherlands, with aims of restoring Dutch republic (or relaunching Cromwellian dream of unifying protestant republics(unlikely Louis would agree to this)), and expansion in Spanish Netherlands.  Dutch probably win naval war similar to OTL 3rd Anglo-Dutch war.  Who has William married? Not Mary Stuart, perhaps the Danish princess Ulrika Eleonora. So potentially the Danes are Dutch allies as a result in addition to the Spanish.  Outcome some limited English and French expansion in Spanish Netherlands, and agreement from Dutch not to make Orange stadtholdership hereditary (stadtholder for life similar to English protector for life). Assume no significant exchanges of colonies. In aftermath William seeks rapproachment with protestant English against France.
Longer term much less Dutch influence on English institutions, in particular in finance. Amsterdam remains centre of trade, not eclipsed by London. So Netherlands remains a great power for longer.

Dutch and English both continue to expand in North America during this time: the Dutch in New Netherlands expand into OTL Pennsylvania, up towards borders of Maryland and Virginian claims;   British establish Cromwellia (OTL Carolina) to form boundary against the Spanish in Florida, populated with many quakers and later Hugenots.  Possibly several colonies along this coast, or perhaps they split later given divisions among proprietors, similar to North/South Carolina OTL.

The revocation of the Edict of Nantes expelling the Hugenots from France is the same as in OTL, but has an even more chilling effect on Anglo-French relations.  As a result the British (as they are increasingly known as) are much more willing to join William of Holland and the Hapsburgs in the Grand Alliance against France.  Nine years war goes ahead similar to OTL, but without James II/William III struggle for Britain, the British are able to field more troops to the continent from Dunkirk, which is heavily invested by the French at some point.  Shortly followed by War of Spanish Sucession.  Probably the outcome of these would be a larger slice of Spanish Netherlands owned by Britain due to stronger British army, coastal strip at least as far along as Ostend, (so it becomes British Flanders instead of the coast of Austrian Netherlands as in OTL). John Churchill is Protector of Britain.  British take Acadia from France.

Domestic British politics evolves somewhat differently. Instead of Tory/Whig split originating over catholic succession as in OTL, division may have come from how to deal with Catholics in Ireland and later Flanders. Tories support freedom of religion for Catholics too, at least in certain areas.  This is likely to also be policy of earlier protectors such as Monck, so Tories are also again party that supports protector (instead of king OTL). Whigs opposed to Catholics, and support parliamentary power over protector, especially House of Commons.   Also a third small force of levellers elected by enlisted men and veterans to House of Martials. Levellers support extension of franchise, not averse to parliamentary power increasing, but only when more representative.  So overall Whig power more constrained by two house system and non-gentry electorate in House of Martials.  Class divisions make it hard for either Tories or Whigs to cooperate seriously with levellers, although political expediency may lead to accelerated electoral reform in the long run.  Levellers can work with whigs opposing catholics, or with tories supporting military.  Rising merchant class (although rising more slowly than in OTL due to Dutch dominance) probably still supports Whigs as prefers idea of civilian government they would elect entirely themselves, so old money landowners again largely support Tories, apart from a cryptomonarchist set who secretly wish for Jacobite restoration. This wing declines over time, though may be secretly supported by France, and they will have last hurrah during jacobite uprisings in Scotland.

Scientific and industrial revolutions proceed similarly to OTL, perhaps with a slight drag due to less advanced financing.

If William III had an heir with his Danish wife Ulrika Eleonora, would the Dutch Orangists have appointed this William IV as next stadtholder?  This would have led to political tensions with the British. Which would have changed early 18th century geopolitics.  British still aim for balance of power on European continent, but between French and Dutch rather than French and Austrians.  Austrians still potentially useful ally having no maritime ambitions.  In North America and India British, Dutch and French all compete with each other.

British don't get involved in war of Austrian succession, being involved as they are in colonial war of Jenkins’ ear (as per OTL) against Spain, and relatively uninterested in dynastic politics.  Hannover is involved with Dutch and Austrians against Prussians, French and Bavarians.

War of Austrian sucession goes as OTL in east (Prussia takes Silesia) and indeed in west where French overun both Austrian Netherlands and Dutch (but even more so than in OTL).  As in OTL Louis XV rather inexplicably intends to hand back these territories at conclusion of the war, but imposes on the Dutch that William V becomes king and marries Louis' daughter, a catholic.  Dutch republican leadership led by an admiral refuse to accept this.  Thus begins Dutch civil war with republicans (aided now by the British) establishing themselves most strongly in New Netherlands, and Orangists aided by the French occupiers in control of Netherlands.  Naval superiority of republicans keeps them independent and influences the initially wavering Dutch East Indian company, with territories from Capetown to points east, to come down in favour of New Amsterdam.  New Netherlands holds off half hearted invasion from New France.  Wave of republic Dutch emmigrate to new independnt colonies via British Flanders.  The admiral who led the war if independence becomes Stadtholder of United Overseas Provinces with new Staten General in New Amsterdam including representatives also from Cape colony, Ceylon and Dutch East Indies.

Going into equivalent of Seven years war (though it starts later and lasts longer han in OTL), Britain no longer has offensive military edge as years of fiscal crisis cut military budget.  Defensively a different matter as territorial reserves maintained.  However, with the Dutch now divided, France remains as the major threat, so a conflict of this sort is bound to happen, quite possibly starting in the same way with French trying to expel Virginian settlers from Ohio valley.  With UOP siding with the British, and Dutch Kingdom with the French, the colonial lineup is similar, and it makes sense for the British and UOP to susidise the Prussians in order to keep French armies in Europe (as in OTL). So overall outcome unchanged, but more likely the UOP in New Netherlands capture Quebec and take over New France, at least the bits bordering New Netherlands.  British take Ohio and Detroit regions, and French abandon claims east of the mississippi. British defeat French in India.  War in Europe same as OTL in East, but French and Austrians conquer and partition British Flanders. Afterwards New Holland (OTL Australia) is settled by Dutch Kingdom with a view to having a base to win back East Indies in future.
William Pitt is British Protector.
American colonist demands for "no taxation without representation" are dealt with better.  Protector Pitt postpones his retirement, and works with progressive elements in the House of Martials to overrule House of Commons intransigence. 
A constitutional settlement is negotiated such that the colonies get to send some representatives (30 for all of the American and Caribbean colonies, the same as for each of Scotland and Ireland) to the House of Commons, and some regiments with representation in House of Martials are maintained there too. London remains in charge of overall imperial policy, including taxes and tariffs by sea, but local administrations can set domestic laws, including trade overland (so lots of free trade to UOP New Netherlands then).  Each colony in addition to sending representatives to London also sets up similar administration, with property owners electing one house, local militia (i.e in practice most white males) electing the other house, and a lord lieutenant appointed from London by British protector, but ratified by local parliament.

Does lack of an American war of independence mean the French are not overstrained fiscally quite as much, thus delay French revolution?  Not for long I suspect.  French garrisons in Dutch kingdom cost and money was borrowed trying to keep UOP in line, and there have still been a lot of wars with not much gained.

To Be Continued