Alexander Graham Bell invented the first police box in America. But the very first British police boxes were built in 1891 to aid the Glasgow Police to better communicate with each other before the invention of the 2-way radio.
How did they work? The police boxes had a light on top that would turn on to let nearby police men know to answer the phone (sometimes a red filter would cover the light for emergencies). The boxes were also available for public use.
What if the TARDIS was modeled after a 1890s police box instead of a 1960s one? This TARDIS is based on a real 1890s police box.
Here it is in 3D: