As has been mentioned, the physical distance you need to cover is very short and baggage comes out quickly. The real variable is queueing time at passport control and security (and possibly baggage drop). At a quiet time, you would have time to do all of this and still have a couple of drinks in the bar before departure; on a bad day, those queues could take 20 mins each.
I've never noticed a separate passport queue for transit passengers, but maybe they'd let you use the non-EU queue, which is usually v short?
Am I being naive in assuming that if BA are willing to sell a through-ticket, it must be achievable most of the time?