As someone who has been at one of those institutions and is currently at the other, I haven't noticed much in the way of hackdays at either... Maybe it's changed at Cambridge, but I didn't see much sign of brewing collaborations at the time (beyond the creative-commons-or-public-domain-only file sharing network).
In Oxford I can recommend Oxford Geek Nights (http://oxford.geeknights.net). It's not student run, but sometimes has students speaking and it's always interesting.
It's improving at Cambridge, but slowly.
There exist Computing and Technology (CUCaTS), Computing Facility (SRCF), Technology Enterprise (CUTEC) and Enterpreneurs (CUE) societies. The latter two have fallen somewhat out of favour and notice around the Computer Lab the last few years, but are still running strong attracting tech entrepreneurs from Physics and Engineering.
There's a lot of focus on moving out to established tech companies (blame the recruitment fair and regular company events) but this outgoing year appeared to have a high fraction of the CS year attempting to work on startups in one form or another.