Booked (via a TA) a bargain basement CW flight to Vancouver in August. However I now I could really use returning a day later. TA inform me the fare's not changeable - at all - fair enough, but will this change at all after I've left?

Whenever I've urgently needed to put a flight back a day post-departure in the past, I've usually managed it - is this worth a shot? Or will BA probably tell me, forget it, you need to buy a one-way ticket home the next day?

Edit... for what it's worth, the Sunday flight, which I am on, is probably busier than the Monday flight.