As stated, submit a subject access request to the DVLA asking who has requested your registered keeper details linked to the vehicle's VRM, when and for what purpose. Turnaround for this is quick usually in a few days or less.
PayMyFuel claim they can automatically retrieve RK data from the DVLA ergo they would need to have a Keeper at Date of Event contract with them if they actually are the entity making KADOE requests. The KADOE contract can be FOId once the requesting entity is known.
If PayMyFuel are not actually making the requests and it is through another organisation that has a KADOE electronic link, the SAR will confirm that and that KADOE contract can be FOId.
It would be good to see the visibility of how these companies make requests to the DVLA.
You should also SAR PayMyFuel to see all data they have on you as given in the scant privacy policy on their website. They state they will no longer respond in that farcical letter so if they don't you can then escalate to the ICO.
With more evidence of the nonsense from this company, a firm complaint to MFG can follow.
Maybe just post MFG a cheque for £24.24?