As others have said, it really depends on where you'll be living.
Also bear in mind that tax, National Insurance, and possibly occupational pension costs will all have to come out of that £25k - if you'd like to work out what that will leave you with, then look at www.thesalarycalculator.co.uk/salary.php which lets you play around with figures. I think you are probably in for a bit of a shock. Years ago at work we had some American colleagues visiting and they couldn't believe the cost of living compared to the salary levels, and it's got worse since. They lived and worked in Washington D.C. as well, so it's not like they were from a cheap part of the US!
To get an idea of what flats or houses will cost, rightmove, zoopla etc are good places to check out; for shared accommodation, spareroom.co.uk will give you some ball park figures. In my experience even when renting the cheapest of flats you will need in the region of £1.5-£2K to cover deposit, first month's rent etc. Without an address history in the UK you are also likely to find it difficult to get a mortgage.
I think you should probably get child allowance (or whatever it's called these days), but I thought tax credits were being phased out anyway? (Someone else can confirm or refute that).
Bear in mind that the cost of living in much of the UK is extortionate these days. Especially in the south, including the south west; hideously expensive these days and many tourist spots have 6 month rental contracts through the winter if you're lucky and then kick you out so the owners can make megabucks during the season. It isn't just the mortgage either, there is also gas/electricity, water, council tax, and other compulsory bills to take into account (e.g. TV licence) and they can easily be another £800 a month. I'm in absolute awe of the PP above whose council tax and everything else is around the £330 mark! I think the amount we pay is closer to the average, though - and that's before taking food, clothing, transport including car maintenance, and leisure into account.
In Cornwall (and most of the south west, even Bristol, Exeter, and Plymouth) you are also likely to find it very difficult without a car or other mode of transport, the public transport is really pretty rubbish when it turns up at all (I've lived a bit further north than that in the West Country since 2005, with a 2 year break, and even though I hate driving there's not really much other option - I have visited Cornwall regularly and our only option has been to drive).
Depending on the area, £25k will go a LOT further in most of Scotland or many parts of the north of England (not York, Harrogate, Ripon, Chester, some bits of Northumberland or the National Parks in Yorkshire, or some other "posh for the north" bits, though - I'm from Newcastle originally and there's no way I could afford to live in any of those areas I've just mentioned. You could afford to have quite a decent although not plush life somewhere like Newcastle or several other Northern cities/locations on that salary.