UK ownership & registration documentation

[popotla]

In Britain, when I lived there many years ago, the vehicle registration document was called the “log book”. In it, as I remember, the owner’s name and address were recorded. If the vehicle changed hands, the new owner’s details were added. In that same document, as far as I remember, a rubber stamp was used (?) to show that road tax had been paid. A paper disc was also provided and this was shown on the windscreen. There was, in other words, one document that provided both proof of ownership and proof of registration of the vehicle (and payment of road tax).

Is this how it still is? Is the one document still used, as above, or are there separate documents (a) to show ownership and (b) relating to registration and payment of road tax?