About 18 months ago, I was booked on the first BCN-LHR flight for the day, ticketed through QF and operated by BA/IB. Got 2hr flight time change about 4 months prior to travel - flight number had been moved to later departure, with new flight number at originally booked time.
Managed to get QF to get BA to move me back to the time booked (new flight number).
Later flight was going to be legal but too tight for my liking connection to QF 10 at LHR so I requested originally booked time.
Note I was dealing with QF not BA. But it is clearly possible. But whether BA “customer service” will do this directly I’m not so sure.