Lots of ways to mix it up if you want something interesting to do along the way. For example, you could fly BA nonstop to the following cities, and then make a connection to SFO:

• YVR, for a brief Canadian experience;
• SEA, for some coffee;
• LAS, for nothing, nothing at all;
• LAX, for some star watching;
• PHX, for a round of golf; or
• SAN, for some time on the beach.

These stopover cities would permit you to travel the greatest distance on BA, thus having the most comfortable Y experience (compared to domestic Y in North America). If you wanted to be a bit more adventurous, you could also try YYC (more Canadians), DEN (skiing) or MEX (thrills). And for something really exotic, you could try LHR-NRT-HNL-LAX-SFO, but I don't think it would be very cost-effective

If you just want LON to SFO without any faffing about along the way, then you'd have to plan a bit more wrt schedules which don't require an overnight. I suppose if you really wanted to, you could try LHR-JFK on BA, then JFK-SFO on AA's transcontinental 762s or 763s…

And finally, for creative use of different airlines, I suppose you could try either LHR-JFK (BA) JFK-YYZ (LA) YYZ-SFO (AA with connection) or LHR-JFK (BA) JFK-YVR (CX) YVR-SFO (AA with connection).

Let us know what you decide!

Note 1: Some flights in the Pacific Northwest can be booked on AS with AA flight numbers, but I'm not sure how that translates into mileage accrual for BAEC members.

Note 2: If booking connecting flights, don't forget about the different airports in the Bay Area, any of which could be useful when planning more creative routes: SFO, SMF, OAK, SJC (and possibly MRY if you want a lovely drive). Oh and there is STS if you want a bit of wine