The blogosphere is enjoying the Government's embarrassment. I think Sir Richard should be fired. He is entitled to his views, but the Army exists to defend the realm and to implement with deadly force the foreign policy of the elected government. He has a positive duty to make his views known to his political masters. As Chief of the General Staff, he will have had ample opportunity to do so. For him to criticise that policy in public is disloyal, to say the least.
There are two possible justifications. One would be if the Government has been trying to use him to make propaganda. If he was ordered to give the interview, then I would entirely respect him for telling the truth as he sees it. This government has "form" for that, at least in relation to the police. Chief Constables have long been reduced to Government mouthpieces and have done themselves no credit by their willingness, nay eagerness, to play politics. They have lost the respect of the public and put an end to "policing by consent." Sir Richard would be right not to make the same mistake on behalf of the Army.
The second would be if he was authorised by his Commander-in-Chief, the Queen. If Her Majesty has tipped him the wink, however, that would amount to a constitutional crisis of the first order. Like my glorious namesake, I am a Republican. Much as I like and respect Her Majesty personally (unlike her idiot heir) I must hope that she, normally so acute, has mis-stepped. That would damage the monarchy as much as Sir Richard's remarks will damage the Government.