They'd have to pick up a decent chunk of the London market to make it worthwhile, interlink traffic generally flies below cost on domestic connections so therefore likely wouldn't make it profitable in its own right. If they were going after the Newcastle-London market then they'd be competing with themselves as they already operate to London City which is far more competitive with the train than Heathrow would be.
Meanwhile there is a business community crying out for flights to London 50 miles down the road where there is no competition from BA...