This answer features the following video clip from the Tenth Doctor era:
An interesting tidbit, from the part where David Tennant is speaking out of character, is the following sentence:
Now I have to talk for around about a minute without hesitation, deviation, or whatever the other thing is. It's like that panel game on Channel Four, like Rory just pointed out.
The panel game he's referring to is Just a Minute (on Radio Four, by the way, not Channel Four). But who is Rory? Obviously not Rory Williams, who wouldn't show up in the TARDIS for another few years after this was filmed. Since he's speaking out of character (as David Tennant rather than the Tenth Doctor), we can assume that this Rory isn't a Doctor Who character but rather a real person, some member of the cast or crew. Do we have any idea who it is?