Of course some of the money spent in London trickles out, if only because it is impossible for any wage-earner (as opposed to a salary and bonuses person) to live anywhere inside the M25, and indeed some way outside it. However much of their pay will go on day to day living costs in London, and if these people were still living at home then all their wages would remain in their community. I don't know if there are any economists on this thread, but I'm sure they could elaborate on this.
Furthermore, one of the reasons these London projects are so expensive is the fat pay packets needed to bring these workers from all over the UK and beyond.