I doubt that any such situation exists today in which someone can offer a large sum of money in exchange for an Oxbridge offer. Oxbridge admissions are very closely scrutinised by both the media and the government, so anyone who did so, or any academic who accepted such a bribe, would be very stupid indeed. Of course, it could happen, but if it did it would be highly anomalous, i imagine.
However, some people would hold that by paying tens of thousands of pounds to go to a private school and be 'trained'* for Oxbridge is buying a place to some degree, although not as corrupt.
It would seem obvious, though, that in a highly personalised admissions system such as Oxbridge's, there would be some weighting in favour of the children of the rich and powerful - surely name-dropping and such like goes on in interviews and perhaps colours it somewhat? It's worth noting here though that Oxford did reject Tony Blair's son, although Jesus Cambridge did allow Prince Charles admission with CCD or something at A-Level (but that was a while ago!).
I suppose the answer to your question really lies in your definition of buying a place.
*It's probably best if we steer clear of the whole 'private school = oxbridge coaching' debate here; suffice to say going to a good provate school substantially increases the chances of a successful application.