England at this point is smaller, has around 1/3 as many people and is less used to the heat. They would not be able to replace the locals and would probably be forced to make more use of native allies, vassals and puppets. The population would seem less mestizo, because they would have a larger pure native contingent.
1) The Portuguese weren't much bigger than England in population but look what they accomplished...
2) How hot do you think Spain is? Only about 1/4 of the country is even hot Mediterranean in climate (let alone arid) and largely only along parts of the coast, most of it being either continental or oceanic (especially in Galicia, which historically exported disproportionate numbers of Spaniards to the New World AND bearing the same climate as Britain). Furthermore, the bulk of Mexico's population lives (and has almost always lived) in the Altiplano highlands of the Center, which generally means less heat, disease vectors or stagnant water bodies. Even if it's a tad warmer than England, it's hardly a tropical swamp in those parts either.
- I picture it looking like Peru, with either mestizos or natives being the biggest group followed by the other one TBH.
EDIT: @Gloss, I agree on the German states (not to mention Scotland, Ireland and perhaps Flanders), though Scandinavia may or may not be too cold-climate inclined; there's a world of difference between, say, London and Stockholm.