Presumably this was a virtual permit, so you typed a '0' instead of an 'O'. The official font for number plates has no '0', the number plate maker uses the same character for both, so an easy mistake and one that has won appeals at London Tribunals, but we have no way of looking at the Traffic Penalty Tribunal statutory register.
If you're prepared to take Bradford there, then you would have a good chance of a win, but you'd have to risk the full PCN penalty. There are no additional costs, and if you win you pay nothing, of course. But first you would have to go through the rigamarole of submitting an informal challenge, (optional), and then waiting for the Notice to Owner. This is sent to the owner's address as recorded on the V5C Registration Certificate.
So, are you the owner ? If not, who is, because the owner has legal responsibility for all PCNs ?