If this conservatory has definitely been there for more than 4 years, the best bet is the Certificate of Lawful Use. The attached link shows how Gloucester City Council explain it - I picked it out at random because it seems to explain it in plain English. The onus is on the householder to apply for and justify the circumstances behind the request.
http://www.gloucester.gov.uk/Content.aspx?URN= 3740#5
I looked at a few of these Council Planning Permission websites that explain the Lawful certificate 'rules', looking for one that stated the 4 year rule that you have heard about and I am confirming. The only one I could find was here
http://www.pcnpa.org.uk/website/default.asp?SI D=306&SkinID=5
This is a National Park Authority in Wales - look at para 3. The same law (Town and Country Planning Act 1990) applies to England & Wales, so I hope that gives you comfort. I take it you are very sure this structure HAS been up more than 4 years?
If you are determined to go ahead with exchange on Friday and your vendor can produce an indemnity insurance policy that will reimburse you for your costs in applying for this Lawful use certificate, then perhaps it is good enough for you. The fees are the same as if you were making a Planning Application - �135 for a modification to an existing dwelling. Otherwise, I'd be asking for about �500 off the selling price for the pain and grief of having to do it myself (its the vendors problem, not yours)