I graduated from Cambridge and there is Oxbridge unemployment, roughly the same levels of it as with other Russell group universities I would say, from comparing with what friends from home have said.
Arts students are more effected than science graduates, but that is because most science grads if they can't get a job pick up a PhD place, whereas funding options for postgraduate study are more difficult to get with an arts subject.
I know very few people who are actually on the dole, but huge numbers who are seriously underemployed. They're working on shop tills and in petrol stations while they apply for something better, but you may not find anything for months or even years in some cases. I know a guy working in telesales, somebody driving an Ocado delivery van, waitressing and bar work are popular.
The other two scourges are part-time work and redundancy. I know a couple of people who have found a job after six months searching, only to loose it again six months later; and again huge numbers of people who want to be working full time, but can only get three days a week.
It's not so hard to get a job in the South East and London, but if you go back up North it becomes very hard. Where my degree is from is a hindrance to finding a job in my hometown, there is no skilled work here and nobody wants to hire an Oxbridge educated receptionist, because they think that you won't stay in the job for more than a week before you're off.
It is harder if you are state educated and have fewer contacts, but having said that people who would normally have contacts have exhausted them all. My dentist was saying the other day that his (Oxford educated) daughter is costing him a fortune doing an unpaid internship in London. He has tried to find her work, but couldn't get anybody closer to give her a comparable internship.
Then there are a lot of people like me, who are doing non-graduate jobs because they don't know what they want, or because they are taking more qualifications and want to retrain. I'm starting a veterinary course, I knew a lot of people going into medicine who spent a year dossing around to get medical work experience, because the only hours they could volunteer in were during the working week or they were working part-time as an HCA.
Basically, we're affected the same way everybody else is. It follows national trends with women and arts graduates being worse affected, and with less employment in the North. There isn't any reason why we would be less affected sadly, you can't get a job if a company aren't hiring.
The only mitigating factor I would say is, it's much easier to get onto a postgraduate course with an Oxbridge degree. I know a lot of graduate entry medics, law conversion courses, pgce courses, you name it - whether they get a job when they come back out of course is still a moot point.