I fly frequently back and forth to Scotland (and London), mostly on the UK airlines. I don't like BA, but I am a huge fan of Virgin Atlantic, and since they now fly into Edinburgh you can take them the whole way. I think in summer I'd jump on $1300 and non-peak times I'd jump on $1100, but $100 or so more isn't a bad deal. If you are inclined to spend a little more, VAs premium economy is great (and much better than BAs). For that think in the $1600-1700 range. On our
ABD trip to Scotland we experimented with Air France and their premium economy seats. I want to say we paid in the $1700-1800 range. I would NOT recommend Air France, for a number of reasons, but the biggest was the horrible connection on the way back: had to take a bus and then a train to get to our connector. We barely made it.
A couple of differences to keep in mind. If you are connecting through London from the US you will have to go through immigration so leave PLENTY of time at Heathrow--3 hour range is good. I almost missed a connection to Dublin once with a three hour window. Heathrow is a great airport, so if you end up with extra time you can pick up a sandwich at Pret or a coffee at Starbucks or shop at the Harrods shop, LOL.
If you connect through London from EDI on the way back, however, you do not need nearly as much time (I've done it with as little as 1 hour between, but 1.5 is better) because no immigration from UK to UK airport.
Keep in mind that if you use one of the US airlines and connect on the way back through the states, you have to claim your luggage and go through customs in the connection city, which is a big pain. I've had bad experiences at both JFK and Chicago, and I usually try to avoid this--although a good deal changes my mind