With Columbus possibly setting up shop in New England or the Chesapeake first, how would colonisation play out without the factor of gold or silver ?
And the part of North America they're likely to hit upon is less promising than the one Columbus encountered IOTL.
I do not think we have to assume that just because Columbus is launching his voyage a few hundred miles north of his OTL launch point that his landing point in the western hemisphere has to be proportionately further north to match.
For one thing, he chose in OTL to take a route down to the Canaries and from there due west to the Caribbean because that went with the current. At the latitudes of New England the Chesapeake, the currents would work against him instead of for him.
Also, he was aiming for what he thought was a prosperous point off Asia, Japan (Cipangu). Further north he would have expected to land in chilly northern extremes of Tarrtary, untold and unadvertised by Marco Polo, and certainly far from any spice islands.
So, Columbus turning south before heading west is quite likely, even in an English-sponsored voyage.
Of course that makes the voyage longer and requires more provisions. However, Columbus likely could re-provision in the Canaries on the way out and the Azores on his return as he did in OTL. England had a long-standing alliance with Portugal and not-bad-at-all relations with Castille-Aragon in the 1480s and 1490s. Religion did not yet set Englishmen and Iberians against each other in this pre-Reformation era, and Henry VII would go on to marry his son and heir to Catherine of Aragon by about 1500.
So the English are likely to first make landfall in the Caribbean, and explore it and the gulf of Mexico in follow-up voyages. From there they will start hearing about Mexico.