They can trace their roots back to 1241 and the reign of King Henry II.
The Royal Military Police (RMP) is believed to have served the Crown longer than any other Regiment or Corps.
Nowadays, the RMP encompasses a whole range of roles; among them one particularly specialist reserve unit.
On the firing range at RAF Akrotiri members of the Allied Rapid Reaction Corps Military Police (ARRC MP) Battalion have been honing their weapons skills.
British Army reservists are generally drawn from a whole range of occupations, but the ARRC MP Battalion is rather different, according to Lt Col Rob Holden:
"You can only be with us if you're ex-military police, police service, or worked at the National Crime Agency."
"Our capability comes from our ability to recruit on a national basis and deploy highly-skilled individuals. Some of these people have 20 plus years' experience."
From the firing range, the team moved on to a mock Forward Operating Base (FOB) insertion and a flight across Akrotiri aboard an 84 Squadron Griffin helicopter.
Created in 1992 the Allied Rapid Reaction Corps is a High Readiness Force that can be deployed by NATO, the EU, or a coalition of nations to wherever it's needed.
In the past, it's taken command of operations in Bosnia, Kosovo and Afghanistan.
Staff Sergeant David Reynolds was a regular soldier for 31 years. He served 19 as a military policeman and re-joined as a reservist just six weeks ago:
"You all have the same working mentality, the camaraderie, the loyalty. I didn't want to leave after 32 years. It was just the end of my career. I thought this would be halfway between being in and fully leaving."
"This was a natural progressive step, and I can give some of my experience and knowledge to some of the younger guys."
In their civilian jobs, some of the RMP officers work undercover in pretty dangerous environments, meaning they can't show their faces.
Corporal Mohammad Asif served six years with the Irish Guards, including tours of Iraq and Afghanistan.
He now works for the Home Office, and was recently invited to visit Mecca as part of a delegation of British Muslim servicemen:
"I want to tell the whole Muslim community that the Army isn't a bad place to work. The Army and religion are both about discipline."