Ref the comments regarding the VOSA check being a check of the vehicles roadworthyness,it isn't. Another,in fact,the proper name for it is a V.I.C. or Vehicle Identity Check,which is to establish if the car presented to them for inspection is the car it is supposed to be,& not one that has been 'cloned'.
The various categories of 'write off',iirc,are:
Cat A & Cat B :The car should have been destroyed & not on the road.
Cat C: Major bodywork and/or structural damage,insurer decided not to repair.
Cat D: Minor damage,insurer decided not to repair.
Cat F: Fire damage.
A HPi check will show if any of the above apply,also in most cases,but not all,vehicles that have had Cat C damage & have already had the VIC check done,it will be printed down at the bottom of the front page of the log book,under the section headed 'Notes'.
The poster above,who said that the seller doesn't have to declare a write off is correct,it is up to the buyer to ask the seller the question as to if the car has been in an accident and is listed as a write off.