Thinking about it, Rowan Atkinson has parodied Doctor Who twice. The Black Adder saga ended with a TV movie called "Blackadder Back and Forth." In that one, the Edmund Blackadder of 1999 wants to trick his friends into thinking he's invented a time machine. He hires a local jack of all trades (& master of none) named Baldrick to build a fake one. Unfortunately this Baldrick is such a bumbler he accidentally builds a real one. Before he knows it the clever Blackadder & his less intelligent companion are wandering through time & space in a box shaped ship that they can't really control.