The constitutional point is that almost everything in the forces answers to the MoD, through that to the defence sec, through him to Cabinet, through that to the PM, through him (in irrelevant theory) to the Queen. The only parliamentary oversight is that both the defence secretary and the PM are (like all ministers) responsible to parliament. But - it's obviously tough to shift a whole defence secretary, as long as the PM backs him and they have a majority. (Especially as in this case he can always plead that it didn't happen on his watch)
So - what? The only way is to keep making a fuss until the parliamentary and media pressure overrides the bureaucrats' advice to ministers to shut up. Once the conflict with the press and the MPs gets bigger than that with the 'crats, something's gotta give. Good luck!