Opposition group leaders on Bradford Council are demanding a public inquiry into the cover-up over the resignation of Paul Flowers.

Both the Conservative and Liberal Democrats have contacted the authority’s chief executive Tony Reeves demanding an independent investigation into who knew what when Mr Flowers’ quit as a Labour councillor in September 2011.

He resigned immediately after “inappropriate but not illegal” adult material was found on his Council computer. The reason given at the time was work and family pressures.

The truth was only disclosed by the Council on Tuesday, in response to questions asked by the media, including the Telegraph & Argus.

Mr Flowers, who quit as chairman of the Co-operative Bank earlier this year, is now facing a police investigation after allegedly being filmed buying drugs. He has also been accused of incompetence during his chairmanship of the now troubled bank.

Those who also say they were not told adult material had been found on Mr Flowers’ Council computer include the Methodist Church for which he worked as a minister in Bradford, Lidget Green Primary School, where he served as a governor, and the Labour Party leader Ed Miliband, who appointed him to a business advisory group.

Liberal Democrat group leader, Councillor Jeanette Sunderland, has written to Mr Reeves demanding to know which senior officers and elected councillors knew adult content had been found on Mr Flowers’ computer, why it was not referred to the Council’s Standards Committee and what actions the Council had taken to make sure he remained suitable as a school governor.

She said: “This must be made public in order to avoid the allegations that they have been complicit in a cover-up.”

Councillor Glen Miller, leader of the Conservatives, also wrote to Mr Reeves saying the Council’s reputation had been damaged and an inquiry would “clear the air”.

He said: “In order to restore public confidence in the Council, we request that a suitably qualified external person conduct an inquiry into the circumstances surrounding Rev Flowers’ resignation including his appointment as a school governor and any other matters as yet unpublished.”

But in response, the Council insists its senior staff had done nothing wrong, that they took “immediate action” to inform the authority’s then-leader, Ian Greenwood, when the adult material was found on Mr Flowers’ computer, and that his resignation meant no further disciplinary action was required from them.

Any further action would have been a matter for Mr Greenwood, the Council said.

Its statement said: “The investigation, suggested by the leader of the Liberal Democrat group, would be a political process, not a Council officer process. The actions a leader of a political group takes in response to one of their councillors accessing legal but inappropriate material on a Council computer is entirely a matter for that leader.”

Council leader Councillor Green said he had already asked Mr Reeves to write a full report into the matter, which would be made public.

He said the report would reveal “what [the authority] knew, when it knew and how it dealt with it”.

He said while the report would not investigate “party political issues”, he urged the Tories and Lib Dems to wait until its publication before deciding whether a further inquiry was needed.

Mr Flowers was serving as a governor at Lidget Green Primary School at the time of his resignation from Bradford Council. The school has declined to say whether Mr Flowers remains a governor, although it is understood he was re-appointed for a four-year term in 2012.

Former Council leader Mr Greenwood was not available for comment.