It's not impossible, but you'd need everything to work well in order to do it, and, at LHR, the probabilities are definitely against you. If you're in C or F and can fast track, that would increase your chances, and if you can travel with carry-ons only, that would greatly increase the chance that your luggage gets there with you. For the record, last time I landed in LHR (in late Jan), my plane was 20 minutes early, there was no line at immigration, and a connection would have been a cinch. But what's the chance of that happening? Suggest you check the next BD flight out, and if it's not too long a delay, switch to it; if it's a really long wait, consider other carriers or take your chances with your original BD flight (among other things, your BD flight could be delayed) and then, if you do miss it, have BD put you on the next one, since it was their schedule change that caused the problem. Of course, if you're going to worry about missing the flight, though, it would make sense to make the change now.