Fast food was a type of food that was made and sold quickly.
When the Cold began their attack on humanity on 2 April 1963, Susan Foreman and some others took cover in a Wimpy Bar. They lived on hamburger buns with ketchup, frozen burgers being the next option. (PROSE: Time and Relative)
Ace and Hex hoped to find a McDonald's when the TARDIS landed in what was apparently London. (PROSE: Six Impossible Things Before Breakfast)
The Tenth Doctor accidentally called Pizza Geronimo in place of UNIT due to their numbers being almost identical. (TV: Planet of the Dead)
McLintock's Candy Burgers sponsored Vator Verse aboard Starship UK in the 33rd century. (TV: The Beast Below)
Torchwood Three often got food from the Cardiff branch of Jubilee Pizza, which had an account in the name of "Torchwood", courtesy of Owen Harper. (TV: Everything Changes)