The Cold War Provost RMP re-enactors don't allow markings to be displayed...
1. Conversant with UK legislation, all vehicles owned and/or operated by Cold War Provost members, whilst on Public Roads, marked as "Military Police", shall have ALL such markings securely and completely covered or where possible removed (see 80 PRO s2 SOP3 below); this includes all blue-light beacons, and "MILITARY POLICE" markings. Where a vehicle owner is concerned over the legislation, it is highly advisable to consult local civilian Police Constabularies to gain advice and guidance.
2. If neccessary, all "Military Police" markings and blue lights may have to be removed prior to accessing public roads, refitting such markings and lights once at the event in question, and removing them again prior to leaving said event.
...though they only give one reference in support of this, and that only refers to the lighting regulations re. blue lights.
Wouldn't the MoD be able to tell you?