Nope, AP1358 Ch 2 quite clearly states:
0228. PCS CU Authorised Ensemble. When authorised to wear and except where a specific order of dress has been prescribed by the chain of command, only the approved PCS CU ensemble, as detailed below, is to be worn. Other items of operational clothing issued for specific operations outside the UK are not to be worn in the UK and NWE. Illustrations and relevant orders of dress are detailed at the end of this section. PCS CU ensemble comprises of:
a. Headdress. When there is no operational requirement to wear a helmet, the service issue beret, with appropriate hat badge, must be
worn by all ranks.
I believe ACM is one of the "all ranks"?
The B Word