I know this doesn't help you directly but perhaps a reference point for others. The later BA5 landing around 11 (12 for us as we were delayed leaving LHR) resulted in an empty immigration hall back in May, and we were the only aircraft to be processed at that time. Having got off sharp from CW mini-cabin on the B789, we sailed through. Had to wait for the lugggage which slowed the process down but if only hand baggage, from leaving the aircraft to getting in a taxi would have been <20 minutes.

I should add, I had the choice to switch to Club Suites on the A350 on the earlier BA7 but wanted to keep the BA5 despite 'old' Club World to improve chance of early check-in at hotel etc. I'd do it this way again as apart from the delayed LHR departure it was all very smooth.