HKG is efficient in immigration, regardless how many people at the queue, it is quick. However, you will need to wait for your luggage. Once re checked in, I guess OP will not need to worry.
OP could also do the check in at the BA counter in the transit area at HKG. They could tag your bag through. It works like a HKIA ground staff will personally find your luggage and tag it to LHR. They will likely to ask u to wait until they found the luggage, normally takes 30 minutes. So u don't have to clear immigration out and in. I believe if you could arrive at the transit desk way earlier than departure, i.e. 90 minutes before, they will not let you miss your flight, and if it is likely you might miss it, they will work out something for u