As at A Level, and I was at Oxbridge. I'm actually the only Oxbridge trainee in my intake though - and the bulk of the lawyers are from universities like Warwick, Nottingham and Birmingham. There's actually quite a high proportion (anecdotally) of non-law graduates, which I found slightly surprising when I first arrived.
The firm has about a dozen trainees over the two years, and yes, we're a fairly sociable bunch! We have a monthly payday lunch, and our firm also puts on end of month drinks (they fill the fridge with alcohol and people congregate in the kitchen after work), which they often attend.
A lot of the work that we do is shaped by the law (insofar as we have to comply with what the law says), but on a practical level it doesn't require detailed knowledge of statutes - just the overview you'll have been taught on the GDL/LPC.
For instance, in Property, you'll likely find yourself helping to draft leases. Our firm has precedents ("templates") with a number of possible clauses in, and you have to tailor this to the circumstances of the client. A lot of this is actually common sense, e.g. an event has to happen within [ ] days - what number goes there? There'll likely be a commonly-used number, but in truth as long as yours sounds reasonable it's usually fine - and the whole lease will be subject to negotiation with the other side anyway.
Similarly, in corporate, you'll be helping with due diligence where one company is thinking of buying another (ie you'll be running searches and reviewing documents to check there are no nasty surprises), helping with the checklist of preconditions to ensure everything is in place before contracts are signed, and drafting the necessary company meeting minutes to show the deal was properly authorised internally. I also found myself doing a fair bit of research (since we act for a lot of wealthy individuals), on things such as whether a UK company can change its "nationality".
I haven't spoken to private client (essentially family law and tax planning) to have a particularly in depth view of the depth of legal knowledge they require, but I imagine it's broadly similar. Will drafting is more about unambiguous language and ensuring the correct formalities are followed - as set down in statute - than very detailed legal understanding. I think the main area which differs is tax, where we have one guy in particular who's extremely sharp - the thing I find a little difficult is the extent to which EVERYTHING is interdependent, particularly when you're dealing with some of the complicated tax structures our clients use.
Apologies for the length, but as you can (hopefully!) see, the work we do is pretty varied and isn't something for which an in-depth legal knowledge is required. I studied approximately 14 different topics at uni, and among the almost completely irrelevant ones are:
Constitutional Law
Criminal Law
Roman Law
Criminal Procedure and Evidence
International Law
Medical Law
...which is quite a large proportion of my degree.