I dont think at 737-3-- could make it from LGW to JFK direct. It might be possible with full tanks, but no pax. From my graph max range with full tanks (16,000kg) is about 3000nm in still air at FL330.
Using a standard day, 58,000kg take off weight, climb from sea level to FL 3350 will take about 17 minutes. Descent will be about 22 minutes. Given that the aircraft is going to be "flying or range" and thus using Long Range Cruise (LRC) power setting cruise will be at about Mach 0.745 (TAS 430 kts approx).
Dont have access to take off or landing data at the moment but i would hazard a guess that Vr would be about 145kts and Vref for landing about 130kts.
Most of the performance charts for the 737 can be found at
www.b737.org.uk