TK already serve the London market out of LHR and LGW, so it wouldn't make sense to also fly from LTN which is almost entirely LCC and charter.
BRS-IST would be a good route to have, although it would affect *A demand through FRA/MUC. There seems to be very intense competition between LH and TK. (LH recently significantly devalued TK flights in Miles and More to match the devaluation of their own flights).
The block time for BRS-IST must be approaching 4 hours. Not sure how much fun that is on a 737. (It's no fun doing transcon US on one). Out of LHR they use 321s and 777s, with occasional appearance of First Class cabins (sold as Business seats).
I guess they'd operate an afternoon flight, for connections to Asia, rather than a morning flight (probably with a nightstop) for connections to the US. I can't see them wanting to do both.
Maybe Simon Calder gets his info from reading this forum?!