There are two considerations here, criminal law and civil law.
It's a criminal offence, under Section 75 of the Road Traffic Act 1988, to sell an unroadworthy car (unless you make it clear that the vehicle is unroadworthy at the time of sale). See here:
http://www.northlincs.gov.uk/NR/rdonlyres/AF6C C87B-9483-4C9C-8F60-2A78AC17C01E/13374/UNROADW ORTHYVEHICLESGUIDANCE.pdf
So you're (theoretically, at least) obliged to ensure that any vehicle you sell is capable of passing an MoT in the state that you sell it (unless you describe it as 'unroadworthy'). Evidence of a breach of criminal law can contribute to the case against you in a civil action.
Civil law, concerning car sales, primarily relates to sales by traders. As a private seller, you're normally safe from the possibility of legal action against yourself as long as you've been truthful in the statements that you make when advertising the car and answering questions from potential purchasers. (However, advertising 'only 30,000 miles on the clock' isn't regarded as truthful, even though it might be an accurate statement, if you know [or have reason to suspect] that the clock has been turned back).
In practice, buying a car from a private seller is usually a case of 'caveat emptor' and the seller is normally safe from either criminal or civil action against him.
Chris