In case anyone else British was wondering, "pumpkin spice" appears to be a mix of cinnamon, ginger, allspice and nutmeg.
I've occasionally seen that pre-mixed and sold here in the UK as "Christmas spice", but I don't think either is a commonly understood term.
The spices, individually and mixed, are used in British cooking. The most recipes that first come to mind for each are cinnamon buns, ginger cake, eggnog, apple strudel. Mulled wine is a good example of using them all together.
Pumpkin is pretty unusual. It's sold for playing with in October, but only the largest supermarkets stock ones you'd want to eat. Squash is available -- I doubt my dad ever ate one, although it's popular with vegetarians/vegans.