What is your bill for - the mortgage valuation, survey or legal work ?
Valuation - if you have instructed this then the work will have been done and the valuation should take into account the class of title as part of the final amount. It may be the agreed price is in the correct region for a possessory title.
Survey - this will look at structural issues and is not really concerned with the property's class of title. Again, if work is instructed by you then it should be paid for.
Legal - the standard process is that you instruct your solicitor, who will then contact the seller's solicitor and request evidence of title and other property information from them (otherwise they could be looking at the wrong property, incorrect boundaries etc). They will then carry out due diligence on the property for you, review title and search results etc and report any issues and potential solutions to you (for example indemnity insurance - have you considered this as an option paid for by the seller (assuming the mortgage company would accept)).
Ideally, your solicitor could have flagged the title issue immediately before instructing searches and carrying out lots of work (which would have kept these costs down), but conveyancing has been down-valued so much now that it is very much an automated process and solicitors will very often only look at the file once all information has been provided - a side rant but it boggles my mind that people will pay thousands for an estate agent to sell their house but want all legal work carried out for less than £1k when you consider the significant implications if the legal work is not done correctly.
Assuming you were "kept in the dark" about the class of title by the seller, then really that is the seller's fault (or their agents/solicitors). My frustration would be directed there and not at my own solicitor/surveyor as they have only done their job (so far as I can see). I would be taking this up with the estate agents (who do not work for you) and complaining but in reality, there is probably little you can do if you do not want to continue with the purchase. If you do wish to continue, then it could be used as a negotiating point to reduce the price.
The sellers are being very short sighted by not being up front about this issue however, as I suspect they may well lose a lot of potential sales if they are not open about it and price accordingly.