LHRTLS would make sense, but with LHR being the way it is could BA or bmi find the slots from somewhere else to fly it - can't imagine that it makes that much money, otherwise AF would have tried to buy the BE slots or move some flights from CDG where they have thousands....
BA do LGW anyway, so can only really see bmi doing it - and wouldn't they need to base it in TLS to make it work for the connections to the world? If so then aren't these the hardest - afterall they don't fly in the ealry morning from Paris which I assume is due to a lack of slots - they only have an early from ABZ after they stopped an overnight in Milan!!!!