That’s not the question and OP didn’t mention Brexit at all. Although you are wrong that nothing new happened following Brexit, as now all UK passport holders need stamping which obviously adds to the processing time, especially at places like GVA.

To OP’s actual Q, queues can indeed get quite bad on departure at GVA. Never as bad as arrivals, but it can give you a bit of squeaky bum time. It varies a lot and partly depends on what other flights are going through at the same time. The handlers do allow for it with boarding timings etc. What I would say is don’t push your luck and leave it to final call to go through.

Also if you have priority pass and the BA flight is going from C gates, the lounges there are arguably better than the BA one (certainly in location) and will mean you can clear the passport worry before boarding.