I read once that spicy cuisine doesn't correlate almost at all with where the spices are native, it correlates with where temperatures cause food spoilage. The theory is that, since chilis, garlic, and onions have some antimicrobial and antibiotic effect, the people who cooked with them in warmer climates tended to survive better than people who didn't, and so passed down their tastes for them more. I read that a bunch of years ago, not sure if it's been confirmed or disproved.

The UK doesn't have much naturally growing spicy things either, and spicy food is still pervasive here.

It's what having virtually no immigration from the east or the med does to cuisine in a country.