BSA C15 250cc
The police version of this popular machine was introduced in about 1964 and reviewed by Bob Curry in 'Motor Cycle' of July that year, where he describes it as a quiet patrol plodder.
It is equipped with a radio-ready tank, a shortened seat, a heavy-duty rear carrier and a 22 amp-hour battery which is charged from its 115 watt alternator. To accomodate the larger battery, the nearside toolbox cover is omitted.
The silencer is special with a mute in the tailpipe, and to keep it docile, the compression ratio was reduced from the civillian spec of 8:1 to just 6.4:1.
BSA C15 1965 EAO4C
BSA C15 1967 ETD17E
BSA C15 CRM290B ex-Cumberland
Note that the Pye Westminster radio seen in these photographs was introduced from 1967. The machines you see on here had probably left police service by then.
The most likely fit would have been a Cossor or Ultra radio if it had one at all, mainly because the radio cost more than the bike.