I doubt that Cromwell's getting into bed with the Dutch was anything more than a temporary thing. Like any good Englishman, he wanted to slag off France and the Dutch would have seemed valuable allies for this purpose. Both the English and the Dutch were aggressively expanding trading nations, scouring the world for sources of raw materials and precious spices. There was bound to be conflict sooner or later.
The fact is that neither the English nor the Dutch had sufficient population to deal with the huge new lands open to them. That's why the English were quite content to have the Germans settle in Pennsylvania, so long as there were not too many of them, and why the Duke of York gave the Dutch of New Amsterdam such a good deal to surrender (Basically replace the flag, stop beating up English settlers and, oh, by the way, change the name - the Dutch took about 30 seconds to realise they could carry on making money as before, and agreed the surrender.)
The land was so huge, the English had to resort to indentured labour, convicts and ultimately slaves to work it.
The fact is, the fertile South was the most important place for a long time, particularly Virginia. The rise of the North was more an American thing than anything the English could influence.