The maximum range of the Boeing 737-800, the most popular variant, is approximately 3,200 nautical miles (5,925 km). The distance between JFK and LHR is approximately 5,900 nautical miles (11,000 km), which is slightly over the maximum range of the Boeing 737-800.
To operate non-stop flights between NYC and London, airlines typically use larger widebody aircraft such as the Airbus A330, Boeing 767, Boeing 777, or Boeing 787 Dreamliner, which have sufficient range and payload capabilities for the route.