I fly to LHR two or three times a year. I find the Skyteam airlines generally the cheapest (especially KL), though AC can be aggressive on price too. Virgin Atlantic often has cheap nonstops, while BA(/AA) and UA nonstops are about the same. (Not clear how the addition of all the US European lift through PHL, or DL (ahem) taking over VS pricing, will change things though.)

Of course, you're actually flying to FRA, and only *A can get you there nonstop...