The English state invests in a strong navy earlier for treasure fleet protection, whether it is run by the dynasty of Henry VII or Richard III, and instead of the English being the early pirates, it is Castilians, Frenchmen, Dutchmen, Flemings who are the early pirates trying to steal from the English.
To follow Columbus's desired route in the right latitudes to approach Cipangu (Japan), he will advocate for making stops in the Castilian Canaries or Portuguese Madeira, or the Portuguese Azores. Once that yields discovery of the Caribbean, England will have a vested interest in being able to continue to use those spots to re-provision, since direct trips from England to the Caribbean aren't possible to supply with the technology of that time. In the beginning this shouldn't be too problematic, because England didn't have any direct conflicts of interest with either Portugal or Castille.
The English would have to generously pay their port dues and the like. I could easily see the English being agreeable to a Tordesillas-like division of the globe with the Portuguese, yielding the eastern hemisphere to them, since the English have no developed interests in Africa or Asia yet.
By the way, this scenario is *only* interesting if the bolded part happens
Pretty much what it says on the tin. Christopher Columbus goes to the England of Henry Tudor (Henry VII) and convinces him to fund a small fleet to explore the great ocean depths. He stumbles into the New World as OTL, but it is England that is first aware of the West Indies and the first one to start exploring the rest of the region, eventually meeting the Aztecs and Incas ...
...by Columbus making first contact with the Caribbean.
When people speculate upon a Columbus getting a more northerly patron, they often assume he *must* take a more northerly route and *must* land much further north in the Americas (tracing the lines of his route x amount north), but that makes little sense, because he had a definite target zone in Asia in mind, in certain latitudes. But people have an allergy to thinking he could go from England to the Caribbean, as if he can only go from an English port to the Western Hemisphere and back, because somehow international trade or stops in other other countries' territory are verboten and every country is autarkic.
Besides, what does Columbus getting to America under English patronage, via the northern route, to New England, or to Newfoundland, get you?
A big fat boring nothingburger, a mere recreation of the OTL Cabot voyages that Henry VIII had no interest in continuing.
