Thank you. from what you describe, there are two principle bases on which they can recover the vehicle. Before we get to that, it would be helpful to briefly examine the legal position. From what you describe, there is no contract in relation to the service provided other than verbal agreement of which both parties will have different versions. Because there is no definitive statement of fees, the consumer rights act intervenes to provide that the fees charged for the service must be reasonable. The amount the company is seeking to charge on the face of it appears to be excessive and is unlikely to be enforced by a court because it is unlikely to be seen as reasonable which is contrary to the term implied by the consumer rights act.
A total company does not have a lien over a vehicle. A lien is a legal right to retain property in certain situations. The most obvious connected with the case like this would be where you take a car to a garage for a repair. This is an example of a legal lien where the garage can refuse to release the car until the bill is paid. Because no lien arises in relation to a tow truck company, there withholding of the vehicle is unlawful and contrary to the Torts ( interference with goods) Act.
In terms of how they may deal with this, there are two principle ways in which they can deal with the issue. The first is to pay under protest using a credit or debit card and then recover the money after recovering the vehicle. The way they can recover the money of paying by card is to contact their bank or card issuer and issue a chargeback on the basis that the amount charged has been overcharged where the only agreed a lesser amount.
The alternative is they could issue whata is known as a Torts claim in the county court using form N244:
there is a fee of £255 which they can seek to recover and they would need to set out in the application that the company has unlawfully detained their vehicle contrary to the above act and for a court order that the car is returned to them. Before issuing proceedings in court, it would be sensible for them to notify the company involved demanding the return of the vehicle and offering to pay what was agreed failing which warned them that they will be applying to court for a court order for the return of the vehicle together with costs as there is no legal basis for them to detain the vehicle