Eureka miniatures of Australia have produced a set of British Army in Aden figures in 28mm scale which actually would do for certain uniforms of the BSAP from the early part of the war until the very end.
I may be wrong but I believe this was riot and patrol uniform worn by all units depending on the situation. Police Reserve and the A and B Reserve also wore this uniform of Dark Blue floppy hat, Dark blue trousers tucked into boots and grey shirt. Early part of the war they would have at least one old style British 56 pattern ammunition pouch on the hip. These lovely figures have two pouches and a water bottle. You could cut some off.
Peaked caps would also be worn with this type uniform.
Weapons such as shot guns, pump action shot guns, 303s, SLRs and later FNs were used by these units.