If your employer will pay for a Y or B fare, United might be the best way to go.

Full-fare coach, even if you have no status, will put you into the Economy Plus section of UA's coach cabin, which gives you a few more inches of legroom. Meals, movies, and beverages (no free alcohol) are the same as regular economy class, however. Both of UA's JFK-LHR departures are redeyes, unfortunately.

If you're flying on a discount coach fare, try AA, BA, or VS on their day flight to London. Economy will be cramped, but at least you can walk around the cabin and you won't have to try to sleep.