I also wondered about this when travelling the same route a month or so back. I experimented in MMB and it did seem as if it was going to allow the change without cost for my semi-flex ticket (which was booked as EDI-LON-EDI, with LON being LCY on the outbound and LHR on the return.) In the event I didn't make the change, though I wish I had on that day as LCY was suffering with high winds.

If you are already checked in, I believe it's a bit more work (and hence time) for the agent to offload you from the flight first, so you may want to avoid doing that.