Former Home Secretary Jack Straw said delays in the 'plebgate' investigation risked bringing the police into disrepute.
He told BBC Radio 4's Today programme: "We're not police officers, we're not investigators.
"What I've said in my letter to Theresa May is that whilst as the Home Secretary, as I know very well, it's not appropriate to seek to influence the outcome of an investigation, it is certainly appropriate, certainly in my experience a lot, to find out what is going on in an investigation.
"In particular why delays are taking place, which frankly have the risk of bringing the police into some level of disrepute and that is a responsibility of the Home Secretary."
More top news
Sara Di Pietrantonio, 22, died in Rome on Sunday.
A vote to remain in the EU will see Brussels exert more power over the NHS, according to the Cabinet minister.
Tuesday: A cloudy, cool and dull day with outbreaks of heavy rain becoming lighter and patchier.