The senior officer remained in post, but faces a meeting on 27 January to be questioned by Police and Crime Commissioner Simon Foster, who has the authority to remove him.
When asked if Foster should sack the chief constable, Streeting said: “He’s got a process to follow and he’s got to do the right thing in the right way.”
But he added: “I find two things absolutely extraordinary about this situation.
“First and foremost that a chief constable misled Parliament and misled the public.
“And secondly, that having lost the confidence of the home secretary, in the terms she set out in Parliament yesterday, that he did not think to act with the integrity that that moment required – to submit his resignation, to offer at least his resignation.
“I find that utterly extraordinary.”
