Plenty of places in London are open all night, but you'll struggle to find anything (other than motorway service stations) with all night or late night food outside London.
In London, if you'll really feel like it after your flight, you'll find cafes open in Soho (famously Bar Italia on Greek Street), Beigel Bake (bagel bakery in Brick Lane) open 24 hours, Tinseltown (burgers etc) in Farringdon, Duck and Waffle (top of Heron Tower - this would be a very cool place to go after a long flight, actually)...