Joking aside, it is inconceivable that the Armed Forces would instigate a coup. The tradition of loyalty to the Crown and pride in Service history is too ingrained.
A mass resignation is possible, such as along the lines of the Curragh "mutiny" (see below). It is possible that any repetition of the Iraq scenario (in Iran for example) would generate enough resignations in the Armed Forces to force the resignation of the government. However, for anything more "serious" the circumstances would have to be astonishing, such as an attempt to replace the constitutional monarchy with a presidency, a major and widespread institutional breach of human rights or the suspension of Parliament by the government. These are without modern precedent in the UK.
I don't believe the Mountbatten/Wilson conspiracy. The story of a drunken rant in Clubland that turned into a rumour is far more believable.
http://www.bbc.co.uk/history/war/eas...ude/pr06.shtml
By March 1914, British government ministers appear to have been considering taking strong action to crush unionist resistance. Sir Arthur Paget, Commander-in-Chief of troops in Ireland, was summoned to London and instructed to move 800 men into the province to reinforce depots and arms stores there. Preparations for a possible rebellion in Ulster were also discussed. It was rumoured that unionist leaders would be arrested. On his return to the Curragh on 20th March, Paget summoned his brigadiers and informed them that active operations against Ulster were imminent. He indicated that officers with homes in Ulster would be permitted to be absent from duty without compromising their careers. Unwisely, he added that any others who were not prepared to carry out their duty were to say so and these would immediately be dismissed from the service. The brigadiers were to put these alternatives to their men and report back; 57 of the 70 officers consulted elected for dismissal. They were led by Brigadier General Herbert Gough who, like many of them, had Irish family connections.
The 57 officers were not actually guilty of ‘mutiny’; they had not disobeyed direct orders of any kind. Nonetheless, news of their resignations caused government alarm. If orders had existed for the repression of the Ulster unionists and the arrest of their leaders, they were at once withdrawn. Asquith claimed publicly that no such action had been contemplated and that the whole episode had resulted from an ‘honest misunderstanding’. The War Office stated that ministers had no future intention of using the army to enforce submission to the Home Rule Bill. This assurance may have been given without cabinet authority, as those responsible for issuing it were subsequently obliged to resign.
Overall, the episode greatly increased the confidence of Ulster unionists; they firmly believed that the government had intended to crush them but its plan had failed for lack of military support. Certainly thereafter ministers were convinced that they could not trust the army to quell opposition to home rule in the province. For Irish nationalists, the events merely confirmed their increasing doubts about Asquith’s real commitment to granting Irish self-government and about his willingness ever to grapple with unionist militancy.