Andy, It really depends on which period you are asking about as the number of available insignia varied over the years along with the authorised establishment.
On 1 September 1963, the Carlisle City Police was formally abolished and
became a part of the Cumberland, Westmoreland and Carlisle Constabulary. Just before that they had an authorised establishment of 124 (all ranks).
Hope this helps.
Carlisle City Police Helmet plates are very rare as there was only about 110 ever made.
Sadly, on integration with Cumberland and Westmorland Constabulary to form Cumberland Westmorland & Carlisle Constabulary, all Carlisle City Police staff were instructed to hand in their 2 helmet plates [black and silver] for them to be destroyed.