Icelandair has San Francisco to London LGW via Iceland for as low as $385 to $462 round trip in June 2018. These fares were hard for me to locate through Icelandair website, yet Priceline, Orbitz and Expedia show these low fares for June 2018 departures.
Priceline ticket SFO – Keflavik KEF – London LGW – KEF (overnight 27 hours) – SFO
$384.61 Mon June 4 – Thu June 14 (overnight) – Fri June 15 SFO
Expedia ticket
SFO – Keflavik KEF – London LGW – KEF (overnight 18 hours) – SFO
$462.00 Wed June 13 – Tue June 26 (overnight) – Wed June 27 SFO
