According to the Sunday Times, EI is in talks with CO to lease slots at LHR, to enable to CO to start t/a ops next Summer. Neither is saying anything. However, leasing slots would presumably bypass the issue of govt approval; no doubt CO would pay very handsomely for the use of such slots.
Re EI t/a services from LHR, I don't see it happening, although even if it did, I don't think govt approval would be required. As long as it plans to operate flights on any route where there is open skies, then the govt could not, legally, prevent them. BFS is a possibility, but probably less likely if a deal with CO happens.
Also reported that EI has requested 4w. slots from BHX to PRG, although even if it does get the slots, it doesn't mean it necessarily has to operate to PRG.