The kind of head start England would have needed would have involved Henry VII bankrolling Columbus when he came calling in I believe 1490. It would have been a very different voyage for Columbus and a lot more time consuming.
Columbus would most likely have been sailing with a Welsh crew that had heard of John the Skilfull's voyage 4 years earlier, maybe even with John the Skilfull as a pilot on one of his ships. So mutiny would not be a worry.
But Columbus would be sailing against the wind all the way to North America and then down the coast, hoping that it was a desert coast of Asia that he could get around on the way to Japan and China.
Columbus would have a much greater chance of sailing all the way to Mexico on his first voyage and reaching either the Aztecs or the Mayas. And that would be the payoff for England, which would start England on conquering the Aztec, Maya, Chibcha and Inca civilizations. Possibly leaving Spain and France to fight over the pieces of what would be left. Yes. That could work.