I had something similar with LH years ago. It took a few keystrokes at checkin, but basically no big deal. If you've got everything in writing, I should think you'll be ok. Is your MIA flight really on the Saturday or the Sunday? (Your first two paragraphs are contradictory I think). You don't have much time to go into London, even if you're on a really early EDI flight and on the 209 to MIA, but that's not my business.