Unlike Penalty Charge Notices served other river crossing authorities, the Tyne Tunnel toll enforcement is under its own bylaws, not the national regulations for road user charges, and the criminal law applies.
If they want to enforce a penalty, the recipient of the UTCN having not paid or appealed, they eventually have to take the matter to the criminal courts, in the first instance this would be the magistrates courts.
Here are the Bylaws: -
https://www.tt2.co.uk/content/uploads/2021/12/Tyne-Tunnels-Byelaws-2021.pdfand more info on the tunnel website: -
https://www.tt2.co.uk/help/prosecutions-code/#:~:text=If%20a%20person%20is%20ordered,all%20other%20avenues%20are%20exhausted.
We see very few Tyne Tunnel cases on here, so there are not many contributors on here with the necessary experience to give considered advice, however, wait a bit to see if someone comes on with more advice.
The real puzzle is why the Tyne Tunnel persists with this legal framework when there is a ready made set of regulations under English civil law, they could use that is fair to both parties.
Personally, my opinon is that your best move is to submit representations and if refused, pay-up. Is there any mitigation that caused your girlfriend to forget ? In the reps, also say you are willing to pay the toll.
The above advice may not be totally correct so, again, see what the others say, but don't miss any deadlines.