For example, I found seats departing New York JFK on Wednesday, November 28, returning from London LHR on Wednesday, December 5.
Other dates are available for travel from late November through mid-May, excluding peak holiday travel. Travel on British Airways is only available at this price for spring travel.
This price is Basic Economy, which only includes carry-on baggage and other restrictions apply for seat selection and ticket changes. A Main Cabin Economy fare is $180 more roundtrip so it will still be slightly cheaper to purchase Basic Economy and pay a $60 each way bag fee if all you need is a checked bag.
Looking for a hotel in London? Here's what's available for the above dates on Hotelwatchdog.