These fares are available on AA, AY, BA, IB, so if you do not like the BA flight YVR-LHR then don't take it. You can do some basic searches on ITA and pull up the fare rules to see the fairly wide range of routings, including through SEA (and a 777 that presumably will have the BA Club Suite).
You can also return to certain US cities and get this down even a bit more ($2300). It is one of the classic transatlantic Oneworld JV fares where if you book AA/BA one way and then AY on the return it will drop a hundred or so off the YQ and if you return to the US instead of Canada it will still give you the reduced Canada YQ and not the larger one that you would get on a US-EU-US roundtrip. I got YVR-LHR-AMS//ROM-ORD to price out like that.