Guards at the royal palaces are made up of soldiers from one of the 6 different guards regiments in the British Army (Grenadier, Coldstream, Welsh, Irish and Scots Guards in the infantry and the Life Guards in the cavalry). These are regular regiments of the British Army and are regularly deployed to combat zones like other regular regiments. Hope this helps.

I don't know if this qualifies as "military power" for you because I'm not sure how you're defining it, but a member of the Scots Guard helped subdue an assailant who fired blank pistol shots at Queen Elizabeth as she rode to the Trooping the Colour in 1981. There is video here: https://www.youtube.com/watch?v=i5FD3-CsMbc