Police caught on camera vans have a vehicle registration plate recognition system which can interact with Swanseas computers systems and get just about any information up that they require.
Also, normal (non traffic/caught on camera) police can get a vehicle check over the radio which advises them of the current owner of the vehicle.
Don't foret the DVLA will sell your full vehicle and owner details to just about any company that wants to buy them for £2.50 a pop, so the thought of police having to fill in paperwork just to do a random vehicle identity check every time they pull someone is a bit extreme lol.
It took them less then 3 minutes to get the full details for my car (including valid insurance and ownership of the car etc) the last time I was pulled, and that was just a normal non-traffic Focus.
If you can get evidence of the car pulling up outside and waiting/driving off when you return etc, such as setup a small video camera in your window and film it on at least 3 occasions, you could go to the police. Of course the only course of action they may be able to take is to wanr the driver of the vehicle that you do not appreciate, which may not be the action you want, but you could ask nicely if they can confirm your suspicions as to who it is (with a yes or no answer to the name you give) and they may just tell you (although it would possibly be a beach of DPA laws).