Here's a mash-up of 'Doctor Who' as might have been seen in 'Only Fools And Horses'.......
Considering Uncle Albert was talking about the movie "War Games", maybe clips from that final story for the Second Doctor might have been appropriate as well. But instead they went with these clips from "Aliens Of London", which occurred early on in the return of the Doctor in his Ninth Incarnation. (Chosen because the term "World War Three" was mentioned, I guess. That was the title of the second half of the story.....)
However, the splainin as to why these characters were able to see events from 'Doctor Who' on the television when they should be sharing the same reality works better with these clips of the Slitheen attacking bureaucrats in the Downing Street offices of the Prime Minister.
Despite the Ninth Doctor's attempts to erase the world's records of his presence from Earth's data banks, there was nothing he could do when it came to the discovery of this "found footage".
From the wreckage of Number 10 Downing Street, video records were found of the attack by these aliens from Raxicoricofallapatorius because the Prime Minister's offices are outfitted with surveillance cameras throughout. So what the Trotters would have been watching was a documentary about the destruction of 10 Downing Street by Clan Slitheen.
This was fan-made, so it has to be relegated to an alternate TV dimension. And as such the "pressure" over whether this splainin holds up is eradicated.....