Lesson 1 of business and law. ALWAYS get proof of posting.
If you are saying that you sold the car BEFORE they say an offence was commited, then just provide proof of the date of sale (ebay listing) and name/address of buyer.
If you are saying that you bought it, sent them a SORN and they didn't receive it, you have a fair chance. Would be much better if you could provide proof of posting.
It has been known I believe, for some less honest people to take a letter to the post office and send it to themselves with a proof of posting certificate stamped by said post office. Then, with a second blank proof of posting, a scanner and a bit of clever work in photoshop, they have produced an authentic look 'original' proof of posting that would confirm sending someone else a letter at a different date.
Not that I woulkd suggest you try that of course, but it wouldn't be that difficult for someone with moderate editing skills at changing dates on post office stamps etc. Of course, one would have to be careful to use the correct post off abreviation of month as they do not use standard ones. ie, May is MY.