American Airlines has a July fare deal at $564 to $571 round trip LAX to London via Las Vegas connecting to British Airways nonstop to Gatwick Airport LGW. There are a dozen or so departure dates in July in the upper $500s and dates in June and July are as low as $519 round trip.
Delta Airlines and Virgin Atlantic had this same route on sale for $569 in July flying Delta LAX to Las Vegas connecting to Virgin Atlantic LAS to London Gatwick. That fare is pricing higher than shown on Google Flights. This may indicate the AA ticket price will rise soon.
American Airlines Los Angeles LAX – Las Vegas LAS – London LGW – Las Vegas LAS – London LGW