Of course the Queen's Guard are a part of the Minitry of Defence's budget because they're a part of the British Army and not a seperate branch of the military like the French Gendarmerie is. The British military has only 3 branches, the British Army, Royal Navy, and Royal Air Force. Another thing is the French Gendarmerie is huge as it employs 104,275 personnel and costs €7.7 billion out of the French military budget Gendarmerie Nationale official site. The Queen's Guard are only soldiers of the British Army that are used to protect the Royal Familily and are not a seperate branch of the military nor a police force. Also I doubt that quite as many British Army soldiers are used to protect Buckingham Palace as the 104,275 strong French Gendarmerie and costs €7.7 billion out of the MOD's budget to guard the palace each year. This arguement is like comparing the Pope's Swiss Guard to the 186,342 strong US Marines branch of the US military. In Northern Ireland soldiers on patrol are merely British Army soldiers and are not part of any gendarmerie, seperate military branch, nor police force. The UK has no gendarmerie or anything like it.