Norwegian Air flights between New York City and London can be booked for $361 round-trip, using a clever (legal) currency trick. Maybe just $338.
Norwegian flies new Boeing 787 Dreamliner aircraft, which feature large windows and a more-comfortable passenger environment than other aircraft.
Checked baggage and assigned seats cost extra.
UPDATE: Maybe only $338, as per http://www.secretflying.com/2016/06/non-stop-from-london-uk-to-boston-usa-for-only-252-roundtrip-vice-versa-for-338/