Free Traffic Legal Advice

Best if you post up the letter from the bailiffs.

This may be a mis-read of a number plate, but you really MUST persist with both the DVLA and TEC. YOu need to get proof of export from the DVLA.

However, have you contacted DART yet, as you don't mention them at all ?  You need to tell them the situation. If DVLA shows the vehicle as exported, they should have a date for this, and this date should be before the contravention date. With bailiffs at your door, the only avenue to get them off your back is to submit an Out-of-Time Witness Statement. For this you need to submit Forms TE7 and TE9. The TE7 is to ask for permission to submit the WS out-of-time.

Speak to the Dart Charge penalty notice department, they are usually quite helpful. I have a vintage vehicle which was "cloned" by an east European lorry. they used the same LLLNNN system we used until 1963.A quick check of their photos cleared the matter.

If you liv in France there's nothing bailiffs can do to collect from there. Quite how Dart Charge got your driving licence details is a mystery as there's no link between driving licence address and registered keeper addresses at the DVLA.

See the sticky at the top of the page on how to post photos.
https://www.ftla.uk/civil-penalty-charge-notices-(councils-tfl-and-so-on)/read-this-first-before-posting-your-case!-this-section-is-for-council-tfl-dartme/

Put the notice on an image hosting site. Just hide name and address.

Bailiffs make their money out of tracing people but this is an odd one.

The VRM on the NoE is CX10YYG - not a French plate but a SORN'd Vauxhall: https://vehicleenquiry.service.gov.uk/VehicleFound?locale=en

Others would know, but this car has not been exported, it's supposed to be sitting off the road somewhere in the UK

Driving licences aren't linked to car VRMs also how could a vehicle be registered both in the UK and France?

But OP you are correct in that your focus should be on how to prevent your mother being hassled. I fear that telling her 'not to let anyone in' won't put her at ease.

IMO, take France out of the equation and look at what remains:
The VRM is still registered with DVLA;
Therefore they will have a registered keeper;
This is you - forget selling a French-registered car in 2023, this is irrelevant. You are still on record as the RK of CX etc.. in the UK;
This VRM used the Dartford crossing..
Hence why you're being pursued...

However, you say that 'the vehicle was never registered there[your mother's house]', but this isn't the point: the car is registered to you in the UK. If all procedural notices have been sent to this address (and unanswered) then they would pursue you, initially at this address but afterwards anywhere provided by the law. You're linking your mother's with driving licence, but we don't know. They might have searched other databases to find out an address.

If you're claiming that DVLA's records are incorrect, then IMO you'll need proof.

A quick look at "Check VED" shows your vehicle status as SORN, and last V5C issued on 15th August 2017. So you should, in theory, still have that paper V5C in your possession.

I think you need to contact DART as a matter of urgency to get details of the vehicle, photos etc. At the moment, the bailiffs have only added on their £75, but if they visit, will add on £235.

"airbed"
??

Dart Charge contact centre is usually very helpful - call 0300 300 0120. Among authorities that issue PCNs they are about the most benign.