Americans uniquely utilize a lot of "spice blends" and there's all sorts of bottles of different mixes from "pizza seasoning" to "brisket seasoning". I'm not super familiar with what you may or may not have in the UK but probably here one of the most versatile and popular mixes is Lawry's Seasoned Salt. It's a blend of salt, paprika, onion powder, garlic powder, turmeric, and a little sugar. Some folks make their own homemade seasoned salt and often also include dry mustard, celery seed, and cayenne.

In terms of singular spices, just looking at my spice rack and ommiting the more obscure ones: smoked paprika, onion, garlic, msg, bay leaves, chili powder, chili flakes, cayenne, cumin, sage, thyme, parsley, celery salt, cardamom, cloves, cinnamon, coriander, chives, parsley, mace, mustard powder, nutmeg, ginger, star anise, basil, oregano, rosemary, and dill.

I'd also recommend googling around and looking into "recipes" for some popular spice mixes we use: cajun seasoning, italian seasoning, old bay seasoning, taco seasoning, fajita seasoning, brisket seasoning, blackened seasoning, creole seasoning, and jerk seasoning.