Virgin Atlantic has relatively low economy fares around $705 to $750 round trip Los Angeles to London LHR or LGW for travel from late August through December 15, 2016.
There are two options: nonstop direct flights on Virgin Atlantic from LAX to London Heathrow or a Delta flight from Los Angeles to Las Vegas LAS and Virgin Atlantic nonstop LAS-LGW London Gatwick.
Of particular note is the availability of $705 (via Vegas) and $731 (LAX nonstop) round trip tickets departing Los Angeles on the Saturday before Thanksgiving and returning the following Sunday (just in time for CyberMonday sales).
Virgin Atlantic Los Angeles LAX – London Heathrow LHR
$731.26 Saturday November 19 – Sunday November 27
Return flight is nearly $170 more than outbound.
Delta Air Lines and Virgin Atlantic
Los Angeles LAX – Las Vegas LAS – London Gatwick LGW
$704.96 Saturday November 19 – Sunday November 27