The picture above was probably meant for a larf, but its mash-up is certainly within the realm of pozz'bilities for the Toobworld Dynamic. (Well, except maybe for the shadow of Darth Vader.....)
"Star Wars" is absorbed into the TV Universe of Earth Prime-Time (and the Tooniverse as well) thanks to George Lucas' pet project (typed sarcastically) "The Star Wars Holiday Special". And even though it took place "a long time ago in a galaxy far, far away", that would prove to be no hindrance for the Doctor in the TARDIS.
Another more subtle link between two of the three biggest sci-fi franchises can be found in this picture:
Bossk the bounty hunter's vest would be the older model. "Star Wars" as a movie debuted in 1977 and its events as I said were "a long time ago" by then. And Jamie MacCrimmon wore the outfit in the 'Doctor Who' story "Wheel In Space", which took place around 2120.
There are some stylistic variations, which would be expected in so long a time span, but basically it's the same design for the flight-vest.
Whoever marketed that design certainly got around!