Icelandair is really pushing their new SFO to Iceland route with August fares to London as low as $283 round trip in August. The deals for summer 2018 start around the first week of August and airfare quickly drops through the month with really low airfare from August 20.
These deals are found through Google Flights search and do not seem to be on Icelandair website. Priceline offers these fares. I booked a $263 Priceline ticket recently for SFO-LHR in autumn.
Priceline ticket Icelandair
San Francisco SFO – Reykjavik KEF – London LHR – Reykjavik (overnight) – SFO