They should issue a charge directly to you as the driver and should, in theory, restart the clock and allowing you to appeal to them and to their IAS if they refuse the initial appeal.
You could then try the IAS kangaroo court but breath holding is not advised. If the IAS refuse the appeal then you will have to wait and see if/when they send a Letter of Claim and then if they issue a claim. They may not but they will have 6 years to issue one.
A court claim is your best bet to get this over with. A judge can decide whether you owe them a debt or not. With a robust defence there is a high probability that they would discontinue before court. If they are foolish enough to try and take this all the way, you have a very good defence with Jonpon v Homeguard.
The evidence shows a stop of only 42 seconds. You must stop saying you were there only “minutes” or more as there is no evidence that you were.
There is no threat to your credit score. If, in the unlikely event it went to court and you lost, you’d still pay less than whatever they put on a claim and as long as it was paid within 30 days, there is nothing on your credit record.
For now, get the liability transferred and then we can take it from there. You are dealing with a seriously, intellectually malnourished company of ex-clamper scammers. If we thought there was little to no chance of beating this, we would not be advising fight it.