You mean England?
England right after the Wars of the Roses.
England whose colonisation of Ireland was still feeble, its control tenuous.
I suppose we wouldn`t see OTL`s good relations between Portugal and England then. On the contrary, the two would become deadly rivals, and Portugal certainly had the better deck of cards with regards to pan-oceanic hegemony at the end of the XVth century.
An English monarch would only be interested if he saw precious metal right away, because royal treasuries were still in tatters; long-term consequences of the 100YW and the ensuing internecine warfare. Silver or gold would be good to have.
But they`d need at least the same amount of sheer dumb luck to defeat and conquer the Aztecs quickly, while the Inca may be out of the question, what with their conquest requiring already established hegemony which England wouldn`t have projected across the ocean around this time period, not after the bloodlet of its aristocracy and not against Portuguese dominance of the Atlantic.
Question is also where Columbus, sailing from England or Ireland, would have landed. If it`s nothing related to gold or silver, then likely no New World frenzy.
If Columbus followed local advice, he might follow the Cod Route. If so, then maybe England`s claims would be - solidly and economically profitably so - over what OTL is called Nova Scotia, Newfoundland, New Brunswick, and maybe Maine. Fishing grounds claimed primarily.
If this is how the New World becomes known in the Old, then the Scandinavian Kingdoms and Navarra might be other players interested to compete, maybe Scotland. It would all be maritime and coastal for a while, then maybe reaching down the St Lawrence.
By the time the whole thing gets off the ground seriously, expect butterflies to have changed Europe`s landscape beyond recognition...