It depends what the house is worth. Is the house priced to sell and therefore worth the £250k? It 's almost irrelevant that you can't afford £250k if that is what it is worth and what the vendor thinks they can get.
Houses here in East Lancs are still moving, I would try your luck. They can only say no. A house that is up for £250k is probably only reasonably going to achieve £235k anyway, so if they say no at £220k, you could still nab it. Being chain free is a big boon, why are they moving? If they are emigrating/found their house already you are in an excellent position.
I am sat in an Estate Agents right now! My Saturday job. I know that here the Manager won't take any houses on that are overpriced or where the vendors are unrealistic. If we had an offer of £235k on a £250k house, they'd be advised to take it.
I;d go in at lower. I really think the market has a way to go yet, the recession is NOT over, people are still losign their jobs and having to sell and house price to income ratio is still ridiculous. So go in at £200k I would. You'll get it for £235k easily I bet.
As a vendor, we didn't really care if someone made a low offer. We just said 'no' amd hoped they went a bit higher!
Having said that, round here in London things are going 5-10% or so under (a recent, realistic) asking price. BUT if they have been on market for a while without an offer, I'd start with 205 maybe? (psychologically sounds better to me than 200?). You are in a great position.