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.