You say 1845. My greatgrandmothers father was a Gloucestershire policeman at Newnham, warrant number 300. They did'nt wear helmets then, top hats and blue tailcoats and white trousers. The next headress would have been a low French type kepi, followed by the British version of the German pickelhaube. The army adopted that headress in 1878 and the police were likely to be same time or a little later.

Roger