United and Star Alliance airlines have Los Angeles LAX to London at $490 round trip for most dates beginning Oct15 -Dec 6 and Jan 8-March 22, 2018. There are a few dates between Sep 18 and October 15 with $490 fares, however, most dates during this period are $576 round trip.
Dublin, Ireland is on sale for $522 round trip with Air Canada, but far fewer travel dates than London. Most low fares are Tuesday departures.
Momondo.com searches may return lower fares for these destinations.
United Airlines Los Angeles LAX – London LHR (UA nonstop) – Zurich ZRH – LAX (Swiss Air return flights).