Of course not. Everyone arriving with London as their final destination has to clear customs with ALL their luggage.

But if you're connecting at London on a single ticket (which seems to be the situation you have outlined), WHY would you be collecting your luggage?

Maybe it's because you have done LGW<->LHR transfers (you mentioned both LHR and LGW in the first post), in this situation because you have to get yourself (and your luggage) from one airport to another, you have to collect your luggage on arrival and bring it on the "transfer". But when transferring terminals at LHR on a single ticket (or even on two different tickets if the check-in agent labelled your luggage all the way to your final destination), you do NOT need to collect your luggage.

Or maybe it's because you think that, like arriving in the US where you have to clear customs at the point of arrival with ALL luggage, it's the same in the UK? It's not.