British Airways has New York JFK to London Gatwick at $473 round trip from April to early June, then mid August to early December, then again in January 2018. The real deal here are late summer tickets in August at $473 round trip for nonstop flights. For $20 to $30 more you can fly American Airlines or British Airways to London Heathrow LHR.
Delta has New York JFK to London LHR prices around $508 for nonstop flights.
British Airways New York JFK – London Gatwick LGW nonstop
American Airlines New York JFK – London LHR – Manchester MAN – New York JFK
Delta Airlines New York JFK – London Heathrow LHR nonstop