Hi
Was the seller the previous owner or a dealer ? I am always put off buying a car from a private seller. If I did I would ask to see a photo driving licence and cross reference with V5 registration document. If it did not match I would not buy. But lets presume the seller was legit but was rubbish at paperwork. You could pay him a visit if you have address. Take a friend to act as a witness if you do this, just in case.
The DVLA must have an alternative form to complete with the details you have, so that you can register in your name. Link below would appear to have alternative form. Check with DVLA if in any doubt. I suspect if there was any problem, once the DVLA had received the form, this would be flagged up.
http://www.direct.gov.uk/en/Motoring/BuyingAndSellingAVehicle/RegisteringAVehicle
/DG_4022310
Good luck. As you say the vehicle has not been reported stolen, so I hope nothing dodgy was involved. The only thing I can think of is that perhaps the seller was in business as an unofficial dealer (not paying tax) and therefore does not want to make himself known to the DVLA. I suspect if his details kept coming up on the DVLA's system, he might have the tax man on to him. ???