To get about an hour more in London, take the train into London, taxi or tube to Paddington, and check in there. I've used the Paddington-LHR baggage service. It's quite reliable and those folks are used to dealing with way-in-advance check-ins. Then, enjoy the city!

(I haven't specifically checked to see if BA has Paddington check-in, but so many other airlines do that I can't imagine they wouldn't.)