It's normally a National Express coach that would be cheapest - and usually by some margin.
And an added bonus is a coach will take you straight to either T5 or the Central Area so no messing about changing trains at least twice which you would have to do if you went into Euston, then either the Tube or HEX to LHR.
There is also a advance booking system for off-peak fares too called "Megabus" - ah, I see somneone just mentioned that.