I fly between the two a good bit and I found the best time generally are during times opposite of school breaks. So months like September, November, January, and February seem to be the cheapest. The most expensive, December, May through August, and the weeks around Easter.
A good route to consider is the Raleigh, NC to Gatwick direct flight on American. They fly a very new Boeing 777 and it's not usually stuffed full and has a few extra seats which means there is at least a possibility of stretching out. Plus immigration is usually quick in Raleigh and the price with a Saturday stay is usually under $600 round trip. In the high season months its $800 or so. I've had more than one American pilot tell me this was about the best route back and forth when you considered all factors, cost, times, and the general trouble with travel that you have and I have to agree with them too.