Storm in a teacup.If youre asked to line up and still not ready, then I'd say you have to give in.You can play for time once.Three times is a bit cheeky.
But the ATCO cant engage crew in a dispute prior departure.Thats a distraction at a critical time.Once it was obvious BA wasnt giving in,she should have shut up and when they were passing 500',she can say she will be filing a report and wish them a good day.
You can taxi slowly to the runway to give the cabin more time.ATC cant really order you to go faster than 10 knots.But once there,you have to be ready or get to the back of the queue if ordered.If its not busy,then no.