To be honest, I'm no expert in this area. Police get DVLA details through PNC so don't interface with the DVLA directly and I'm not traffic.
With that said, I think I could give a bit of a steer. The DVLA should be assessing each request on the merits of the request. I don't know the process for this but it makes it highly unlikely that they'd block access to information on what the DVLA deems a legal request for a normal member of the public. It might be possible for national security reasons, but this is obviously not applicable. It's also highly unlikely that the DVLA would tell you who they've disclosed your details to. They might at best tell you how many requests they've had as part of a Subject Access Request, but they won't give personal details of who requested it.