In the UK, your car has a title which is proof of ownership and you never even know this document exists, let alone have possession of it.
Proof of ownership of the car is called "Manufacturer's Statement of Origin" sometimes called the "Manufacturer's Certificate of Origin". The actual title of the automobile.
The registration process involves you signing the form allowing the dealer of a newly manufactured automobile to act under the "Power of Attorney".
The dealer sends the Title to the Driver Vehicle Licensing Agency (DVLA) where they take a copy and destroy the original.
The copy of the Manufacturer's Statement of Origin is not a document for proof – only the originals are. This allows the government to own the vehicle making you the "registered keeper".
Since the original documentation has been destroyed there is no way of proving ownership in the future. You have also registered the automobile as a commercial "vehicle".
This is why the Police always say "vehicle" instead of car. Since the car is now owned by the UK government as commercial machinery, the operator is required to have training and a license to operate it.
The government, now owning the vehicle can seize and impound it. If the car is owned by you then this would be classed as theft by the government.
The Department of Transport trades as DVLA.