Virgin Atlantic and Delta have San Francisco to London LHR as low as $579 round trip for flight departures from November 9 through May 10. There are even some low fare dates during the last week of December. Some of these low fare deals are nonstop flights in both directions flying Virgin Atlantic and other itineraries involve Delta flights and a USA domestic connection.
American Airlines has SFO to London as low as $672 round trip. Star Alliance airlines are $700s.
Virgin Atlantic San Francisco SFO – London Heathrow LHR nonstop
Delta Airlines San Francisco SFO – London LHR (VS) – Minneapolis MSP (DL) – San Francisco SFO (DL)
American Airlines has SFO-London on sale for $672 round trip.
American Airlines San Francisco SFO – New York JFK – London Gatwick LGW – New York JFK – SFO
Star Alliance is in $700s at time of this post Oct 12 7:00am California time.