The Paddington Newspaper train was not unique.
I spent a summer (1974?) working for John Menzies Wholesale in Leeds. We used to get a train with London papers at around 2.30am, but quite a few nationals also had presses in Manchester. We had a few early Manchester papers for those newsagents that opened very early, and these and the Londons were taken to our warehouse for sorting.
The main consignment of Manchester papers came in around 4.30 am having been sorted for delivery on board. The packers travelled across to Manchester around 11.00pm the previous evening, and the vehicles, I seem to recall, were dedicated GUVs which were signwritten 'Newspapers'. They had trestle tables to work on, but no specialist internal fittings comparable to a TPO. There was one vehicle each for John Menzies and W H Smith, and both London and Manchester trains also carried mail. They unloaded on what was then Platform 5 at Leeds City (now 8c), and we used to back the vans up to the platform edge to load directly. A novice train driver would come in for some stick when the doors didn't line up precisely where the vans were waiting.
For some reason the Sunday night/Monday morning London train always came in reverse formation, with the newspaper vans at the rear (now Platform 8a)rather than the front. It could be interesting with the WH Smith, John Menzies and Royal Mail vans all jockeying for position, and I was told that tempers could fray in December when the Christmas mail made things even busier.
BTP always magically appeared to greet the paper trains before melting away again with their complimentary copies!