I would like to know what legal rights they have regarding Privacy regarding video recording whist they are responsible for the car. Thank you.
I think, as the owner of the recording equipment and vehicle, you are responsible for keeping the footage secure and not accessible to any unauthorised persons, and you have a legal duty to do so. They should not have had access to anything not recorded by them. There are exemptions for personal use, but I don't think you can avoid your responsibility to keep the footage secure.
I think it is fine for them to unplug the dashcam or remove the memory card if they want to, while they are responsible for the car, but deleting footage means that they have accessed video from other times, and they shouldn't do that, but I think is your responsibility to prevent them.
So you should have swapped to an empty card when you arrived at the garage, then there would be no privacy issues.
Obviously if you want to be certain about the law, you should consult a lawyer, but I doubt you would get a useful answer, largely because most issues like this one have never reached court, so there is little useful case law yet.
On the issue of if it was OK for you to record them, which maybe what you are asking about? That does not seem clear, but in general, the car was probably in a publicly accessible place, so I assume the law is the same as out on the streets. That is a bit questionable, needs someone to take it to court and find out, but most garages seem to treat dashcams in that way. The only real issue I see is in what you do with the video that is recorded, and I think you certainly shouldn't upload it to youtube without their permission, it should be deleted, probably by loop recording, unless there is a reason to keep it, in which case it should be accessible only to you, and maybe the police. The garage doing the detailing work may be a bit different, since it may not be considered publicly accessible, while any MOT garage, you do have access to, or at least to their live stream cameras so that you can personally see what is happening.
What you should ask yourself, is why did they take the time and effort to delete the footage? Most garages do not do that.
You probably don't want to use them again!
If you are not going to use them again, then an enquiry about the deletion may be interesting, even if not useful. If you do want to use them again, I suggest you forget about it, enquiries are not always forgotten and can have consequences.
