The J product on BA is top notch, even if LHR was as bad as people say I'd still risk it. Assuming your return from LHR is on a 747, see if you can wrangle two seats up in the upper deck, it feels almost like you're on a private plane up there.

I last went through LHR in July, I wasn't subject to the sizer going out or coming back, and lines were entirely reasonable at the FCC. Go through with the trip, I'm sure you'll have a great time.