Alf,
Here is one coming out of undercover, however temporary.
Never worked from a police box of Tardis fame and I cannot recall one being in Brum. That is not to say there was not one but I never came across one.
I worked uniform at Kenyon Street, Part of the 'C' Division covering the Hockley area.
We had the metal boxes which consisted solely of a telephone gained by the small door on the front (lockable) Beneath this was another compartment in which one kept one's cape mainly, easily obtainable should it rain when one was out and about.
As memory serves me we had two such boxes. One at the Parade and one at Spring Hill.
We performed traffic duty at both The Parade and Hockley Brook and yes those white macks were rubberised and hot. When doing traffic at Hockley Brook the dairy nearby used to do a roaring trade selling bottles of milk to us.
One was posted to this duty, subject to ones shift, between 8am and 7pm There were two of you involved and the other officer patrolled the adjacent beat ensuring that he relieved his mate on the hour so he could get out for five minutes from the traffic fumes. He did his stint at it between say 10 am and midday and on the next shift between 4pm and 6pm and you relieved him in that period. Became a true slog if he got tied up with a job and could not give you a break. I remember on Hockley Brook one day I was stuck for four hours there. My oppo had got involved and they forgot to send someone to help me out. Think I had two bottles of milk that day when relieved.
One bonus on Hockley Brook was the conductresses on the buses would pass you sweets as the bus slowly passed. They were needed to soften the dry throats.
Came across large shed like police boxes (larger than the Tardis type)_ when I came down south. They had cooking arrangements let alone the compulsory kettle. Lockers and desks. Offices in themselves.
I never used them for on the hour every hour all the bobbies from surrounding beats would congregate there. My outspoken view of them was that all the local villains would know they could pull a job on the hour and get away with it more than like for they knew where the constabulary were.
Oh well memories now back to undercover