No way in hell is the UK going to give something to Russia in this particular case. I mean, just imagine the situation if the UK now pulls of some sort of exchange with Russia for this guy: he's going to continue denying that he did it, even if found guilty Russia will deny all allegations and accuse the brittish government for orchestrating these false charges, they get to have Litvinenko dead AND they get something else in return for someone they don't really care about anyway.

Fact of the matter is, Russia trounced on the UK's sovereignty and did it with a lot of noise. The UK essentially got humiliated and they are going to have to apply negative leverage over Russia in order to get that guy in order to save face. Since the UK actually is a lot more powerful economically speaking and have a lot more say in organizations such as the WTO and EU they are in a position to put a lot of hurt on Russia for this, if they would really want too.