Sounds like you're on a losing battle, because the fine is already paid, they'll just use any technicality to refuse to refund it, the last of which will be that by paying it, you've admitted guilt/responsibility. I get why you paid it, to prevent it doubling, but paying anything to anyone who demands it, automatically admits responsibility/liability, that's exactly why they (govt, police, corporations, etc.) offer you the lower amount if you just abide by it and pay it up front, with a threat that it'll grow if you don't and threats of legal action being taken against you, with added court costs, etc. to encourage that 'admission of responsibility' when people don't want to get caught out. Simple fact is, you didn't own the vehicle at the time the offence was committed and therefore the fine wasn't payable by you, if you could provide proof that was the case, the worst they could chase you for, would be the offence of not notifying them of the change of ownership, which in my experience they rarely actually do. Even if they took you to court for the offence of being uninsured, a judge would likely dismiss the claim before it made it to a hearing, because you'd proved that you didn't own the vehicle at the time, DVLA would then have to bring a separate case against you for not declaring the change of ownership.