How do I know that a) they want it and b) can comply with it
Well I'm assuming here (sorry if I'm making unobvious assumptions) that the aircraft has told London Info its routing info in the way that any aircraft would on first contact and that they could retrieve the flight plan...which would show an airways routing on it. I know London Info will not have the flight plan immediately in front of them but they can get hold of it relatively easily...
I think we are perhaps making more of this than it warrants...in the end it comes down a basic principle of dealing with ATC...if in doubt...ask