I'm of the school that 2:10 is more than enough time assuming you arrive no later than 1:45 before your next flight. You can get AC to check your bags through and issue you a BP to EDI at check-in or in the MLL (if the check-in dude is too lazy to do it). You will clear immigration at LHR and customs at EDI. Depending on the flight you are on (read: time you arrive), you should be able to clear immigration within 15 minutes of entering the line-up, but summer holidays aren't entirely over yet in the UK and international students will begin arriving shortly -- so they will generally keep the lines a little slower moving than normal... Fast track will get you through in 5 minutes probably.

I typically leave the Arrivals Lounge no later than 45 minutes before departure as I'm a fast walked and know the quickest route to T1. Maybe you should have at least 55 if it's one of your first times or if you're a slower walker.