If you have a look at the 2009 employment report of LBS you see that they placed 9% into PE / VC. I think the employment reports of Oxford and Cambridge only mention placement into finance (44% and 25%, respectively), without breaking it down into subsectors (at least I couldn't find this information). Placement into PE is generally difficult, and I think it is even more difficult from a European MBA program simply because most PE jobs are still based in the US. Unless you're currently working in a pre-MBA role at a PE fund or in IB at a top BB I would be more concerned with placement into IB than PE.
Out of the three programs my guess is that odds for PE placement are slightly higher at LBS. As mentioned by others, all three schools will give you a decent shot at IB. Besides placement I would think though that LBS has a significantly stronger alumni network in finance (due to larger class size, higher relative placement into finance), that's maybe worth considering as well.