Oneworld member British Airways offers cheap nonstop flights from its hub London Heathrow to Reykjavik, starting at €82 / £73. This is a base fare that does not include luggage. Adding a checked bag up to 23kg adds €35 on ba.com, which is still a very low fare.
British Airways operates A320 family aircraft between London and Keflavik airport.
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We were not able to find any fare rules for these flights. It seems like they are available from January through March 2020. Since these fares are most likely based on availability, we recommend that you act quickly, if you want to take advantage of this offer.
These flights are sold exclusively by British Airways on their website ba.com. You can use our availability calender to find suiting dates for trips between three days and two weeks: