The websites talk a lot about haulage and obviously the recovery breakdown sector is a bit different, so does one need all the same documents if going into the EU to collect a broken down car
The driver and recovery vehicle would need the same documents as in:
Vehicle being towed/carried back would count as means of transport Regulation 25 CIDEER which allows by conduct declarations for Part D (Oral by Conduct List) goods. So on return to the UK a Customs declaration will be required but at most locations the declaration can be made for the free-circulation procedure by conduct for a means of transport if a relief from import duty is available. A relief will be due if the vehicle was previously in free-circulation in the UK.
When boarding the ferry the haulier will not need a GMR before 1 January 2022 but will need to confirm (in T&Cs for passage) that the declaration requirements are being complied with.
The conduct that is required is that the vehicle disembarks from a vessel and driven past a Customs office. If stopped by Border Force officers, drivers should advise that a declaration by conduct has been made for these vehicles
At the EU side of the EU-GB journey it should be noted that UK owned vehicles that are returning to the UK from the EU (including broken down vehicles that are towing an empty vehicle would need to comply with the Union Customs Code. For example French Customs guidance should provide details on what is required to get these vehicles through the French border although goods which are deemed to be declared for release for free circulation procedure include, “means of transport which benefit from relief from import duty as returned goods” [Article 138 (3) Commission Delegated Regulation 2015/2446]