Welcome to FT BuffaloBob!

I am not sure about your specific situation, but in general, international arriving passengers collect their checked bags before proceeding through US customs. If the bag is checked through to Buffalo, you would drop it at the baggage recheck, otherwise you would need to go to the JetBlue counter. In either case, you have to go through security again, as you've had contact with your checked baggage.

The exception to this would be departure points where they do US pre-clearance (you go through US immigration and customs before boarding your originating flight), I don't think they do this at LHR, but I could be wrong.