Anarchy in the UK?

So, immigration minister Beverley Hughes was forced to resign and now the Home Secretary is under pressure from the media and opposition, all as a direct result of a civil servant "whistleblowing" to the opposition.
Now the Government has recognised the worrying nature of this sort of development and launched "whistleblowers’ roadshows" (heaven help us) in order to provide a route for concerned civil servants to air their concerns. Or, in other words, to give Number 10 a method of controlling these sorts of events and managing them, rather than giving the initiative to the media or opposition.
It does represent a worrying development though. If a civil servant can act to bring about the resignation of a minister, albeit a reasonably junior one, then that suggests that the civil service as a whole could do considerable damage to an incumbent government, whether that be in the general public interest or as an act of malice or political opportunism. The result of this would be an ungovernable nation, as the infrastructure that administers would, in itself, become unadministerable. The political and governmental instability that would result would lead to dire social and economic consequences.
So, the question is, how does one strike a balance between the need to keep the civil service truly impartial and apolitical, as it is always supposed to have been (though I doubt that the reality matches that ideal) and the need to allow legitimate concerns to be raised and dealt with in an effective manner, without causing sensationalist reaction before such concerns and allegations are proven?
Answers on a postcard?