I don't know for certain but I'd be extremely surprised; apart from the fact that it would mean going up against two carriers with lower cost bases than theirs.
The main reason, however, is that BA is having enough trouble keeping its fleet of 734s going; they regularly have to hire in acft from Titan and others. Having visited LGW quite recently, it seems to be 50+% Easyjet and I can only see that trend continuing; ultimately, I see BA winding down its short haul presence, not increase it.