We bought a house from a vendor making the same stipulation about price, hence massive alarm bells. We understood it to be because they wanted a quick sale (they were also naive about the market and unwilling to accept value had dropped) but the other possibility was of course that they had something to hide that a survey might discover. This turned out to be the case - one big expensive thing and quite a lot of other things that we've discovered along the way.
Unfortunately our survey did not discover the big problem (costing us about £10k) and missed some obvious smaller ones (£1-2k each to a total of about £8k). This was a Buildings Survey (structural survey - top of the range and definitely what you need in a case like this) and we are currently taking action against the surveyor.
What kind of survey did you have? I think you'd be mad to go ahead without a Buildings Survey.
Can you afford the sort of extra costs we've paid, or much, much more, depending what other problems there might be? Would you still think the house was good value at the agreed price plus the possible, unpredictable, costs of repairs?
Our vendor had lied in a conveyancing document. I could have taken them to the small claims court for misdescription but decided it wasn't worth the hassle and there's no guarantee of payment even if the court found in our favour.
I'm currently taking a case against the Council to the local authority ombudsman, having been all the way through their own complaints procedure because, in our case, a building regs certificate had been issued for work that hadn't been inspected properly and never did meet BR standards - inspection deliberately prevented and worst bits hiden by devious vendor. This won't win us money and our complaint may well not be upheld but I feel the point needs to be made.
The surveyor is the person it is worth pursuing financially, as he is insured and regulated, so there's a mechanism for assessing competence and accessing payment. Estate Agents would be the same.
It's standard for your surveyor to flag up anything that would have required building regs (small works need this but often not planning permission) and for your solicitor to do the chasing with the council and ask for insurance if needed (and yes, this can be for work going back decades, though, if the work was ok as most is, enforcement action will never be taken, hence this insurance is cheap - but the vendor should pay it).
I hardly need say that all this has taken up a great deal of our time, as well as money. Are you prepared for that?