Police boxes started to appear in 1880. “Modern” police boxes, like the one in Doctor Who started to appear in 1920. A police box was a telephone for the use of members of the police. Police boxes were before two-way radios.
Police boxes have a telephone that is linked directly to the local police station, allowing officers to keep in contact with the station, reporting anything unusual, requesting help, or to detain prisoners until a vehicle could be sent. This was a time when the officers walked or rode bicycles rather than use a car.
There is light on the top of the box, which would flash to alert an officer that he should contact the station.
Members of the public could also use the phone, which was on the outside of the box, to call for help.
"Quick use the police box to call for help"
A big blue box used up to the 1960's to temporarily hold criminals in.
Now known as the TARDIS.
Man: Hey! He stole my money!
-Man takes back wallet and forces thug into police box-
The Doctor: Whot?
Thug: It's bigger on the inside...