The search to show it up would be a coal mining search. These are usually done (though rarely found in HIPS - usually just a local search and water & drainage search) but only required in certain areas.
Where about are you and I will check if it's an area covered (you can also check yourself on the coal authority gazetteer.
http://www.coal.gov.uk/services/miningreports/ index.cfm
An environment search would have picked up if it was in a coal mining area but not the location of shafts.
Bear in mind that in certain areas, different searches may be recommended such as Brine in cheshire and Tin and such in Devon and Cornwall.
Who is telling you the mining shaft is the problem? Is it something known locally or due to publicity of some kind or something that has affected nearby properties?
Alternatively, has any problem been disclosed on the protocol forms (Seller's Property Information Form/Buyer's Information).
If a coal search was done it would have given certain information (they come back very quickly so I'd imagine done from computerised records as is the same with environment searches now).
The site also has some info on certain problems associated with mines and such.
It might be that there is a shaft which is not a problem from the coal authority's point of view but may be offputting to purchasers, possible revealed on, for example, an environment search (subsidence, ground instability etc...) or again by local knowledge or problems or similar.