No actual knowledge, but I bet "registered" companies that fulfil requirements about data security will still get he info, but it will tighten things up on smaller "iffy" contractors.
What I find more interesting is that case a few weeks ago about a food delivery driver harassing a client with phonecalls/texts. The parent company appeared to be wiggling on that one, but where they give sub-contractors contact info, they must still hold responsibilty.
In that case the customer gives permission for their information to be given to the delivery driver so Deliveroo hadn't done anything wrong, the fault lies with the delivery driver who should only use the info for the purpose of delivering and then should delete the information if its held on a device or securely destroy it if on paper. there was a case a while ago where a large pizza chain through all the customer print outs in the general waste bin, iirc they got fined a very large amount.
As for 'parking fines' (yes I know they aren't fines) I suspect that they get around it by the fact that when you enter a car park you are entering into their contract which states they will get your info from DVLA.