Let's see:
Accommodation: The prices vary between £2280 and £5655 for the year for first year undergraduates. A fair average is about £3500. And that covers gas/electricity/water and also gives you insurance for stuff in your room. Check out
The Warwick Accommodation Thread for more info, including the guide on the front page.
Let's say that leaves you with £4500 for the rest of the year. If you set aside £1500 for books/cooking stuff/laptops at the start of the year, you are left with £3000 for the rest of the year, which is more than enough. Food should definitely cost less than £25/week, but you can get by with £10-15 if you really want. The average is about £15-20/week. Going out will probably cost you the most, if you want it to, but it is up to you how you approach it. The more you go out (particularly to Leam) the more expensive it can become - I've spend £30+ in Leam in one night (including a meal beforehand) but if it goes horrifically wrong and you lose everyone, a taxi back to campus burns a nice £20 hole in your wallet (obviously if you share in a group it will be £4-5 each).
One off expenses at the start of term: around £55 for the Freshers Fortnight pass (access to the first two weeks of SU events), £45 for Warwick sport, another £93 for the Gym, or £36 for the weights room for £57 for the climbing wall. Prices may (and probably will) go up slightly for next year though. Additionally, you can join societies for about £5 each, after you pay £10/year to join the societies federation, which allows you to join all societies.
Other expenses that may occur during the year: Trips: sports clubs to tours around the UK/abroad - these might cost a few hundred pounds each, depending for how long and where you are heading off to. Clothes: yeah, you could budget for that if you like as well. But you don't need to go on tours if you don't want to.
In summary, I didn't spend £1000 a term on things outside of accommodation or tuition fees, probably more like £750 in the first 2 terms, and I went out quite a lot. Additionally, around term 3 people revise more and go out less, at least until after exams, so you spend less over that period. I know people who get by spending £500 a term, so living on a tighter (but not restricted) budget is possible.
But remember, what you get it isn't all free money - you have about £3500 of loans that you have to pay back sometime (albeit once you earn over £15k), and remember things may happen down the line that may cost more, so always be wary of that. You also can get a good overdraft though, for example with Natwest you get £1000 overdraft + their free 16-25 railcard. So that could be a good backup.
Finally, living off campus in second year is more expensive, I believe. You have to add a £250 bus pass (if you are in Leam/Cov), pay for gas and electricity and pay deposits and administration fees (no admin fees/deposits with Warwick Accommodation though). Next year I'm going private but have already spent £1050 on the house in deposits, rent and admin fees, so keep that in mind. But this year I'm paying £2800 for the house - which isn't bad. Don't forget with off campus you are getting 10-11 month lets so that adds to the cost. If you get a cheaper accommodation (less than £3500) you won't need to be looking to save that much money to cover the fees (I'm an extreme case since the place I'm living in next year is £300/month - quite expensive and I've had to pay 2 months rent as my deposit instead of 1). These fees won't need to be paid until April/May, but keep them in mind if you decide to go with a private agent instead of Warwick accommodation. I'd say keep your overdraft as clear as possible for when the time comes
If you do need a job,
the SU and
unitemps will be a good site to keep an eye on