@Tupp_ed
Doctor Who first aired in 1963, when police boxes were more common.
https://en.wikipedia.org/wiki/Police_box says:
In the show, although a TARDIS is normally capable of disguising itself to blend in with its surroundings, the ship's chameleon circuit broke down in England in 1963, and left the TARDIS seen most often in the show stuck as a police box.
as police boxes were phased out in the 1970s, over time the image of the blue police box became associated as much with Doctor Who as with the police.