There are two reasons, according to one young officer, why the structure of the British Army would make it impossible. Firstly, the Army is made up of many competing Regiments. Without political masters, the Army would collapse under the weight of its own in fighting. The Army is dependant on politicians for leadership, as much as the politicians are dependant on the Army for the protection and security of the UK.
I thought it was interesting that officer cadets were being encouraged to debate this topic. As the program concludes, the very system (Sandhurst) that trains our officer cadets makes the possibility of a military coup impossible.