I once sold a moped on ebay, the guy picked it up filled in the new keeper slip and I sent it off.
However a couple of weeks later the moped was caught in a bus lane on camera and was sent the letter with a fine.
I got back to TFL (who issued the bus lane violation ticket) and told them the moped had just been bought by someone and it should now be registered to them.
They then contacted the DVLA who confirmed that the keeper had changed and all was good.
When you sell a car and notify the DVLA you should get a letter saying that you are no longer the registered keeper, I always keep these letters as proof incase something like this happens.
Best case scenario is that you can prove to whoever sent the speeding ticket (local Police or local authority) that you weren't the owner at the time, in which case you will hopefully get off without the speeding ticket or fine.
But you'll just have to suck up the £650 fine and points from the DVLA as you clearly failed to notify them of the change of keeper.
You might possibly be able to plead ignorance or forgetfulness. But to plead ignorance it would have to be the first time you've ever traded/sold a car. And to plead forgetfulness you would have to show that you hadn't received any letters from the DVLA about renewing tax in the months since you sold it (how long ago?) and that maybe you had been too busy with something like an illness or death in the family.
As suggested, talk to citizens advice but be prepared to pay up. You may be able to get the fine/points reduced, but it may take some time.
Good luck.
