The Department for Education and Birmingham city council are failing to quickly repair the schools damaged in the Trojan Horse scandal, after a series of snap inspections found little progress at five of the schools involved, Ofsted’s chief inspector Michael Wilshaw has said.

The inspections, carried out only a few days into the start of the school year, highlighted weak management, mistrust among staff and continuing gender segregation among students at some of the schools, as well as reactions from parents at collective Christian worship being imposed on the largely Muslim student body.

In a letter to education secretary, Nicky Morgan, accompanying the inspection reports, Wilshaw said the government needed to take more rapid action to fix problem academies, and criticised Birmingham city council for failing to reveal its plans.

Inspectors last month made no-notice inspections of the five schools – Oldknow, Park View, Saltley, Golden Hillock and Nansen – that had all been downgraded to “inadequate” after an investigation triggered by allegations of a “Trojan horse” plot by Islamists.

The Ofsted inspectors deemed the improvement plans produced by the school leadership, trustees and the council to be “not fit for purpose” at all of the five schools, despite the involvement of the DfE in several cases.

Brigid Jones, Birmingham council’s cabinet member for children and family services, said that only one of the five – Saltley secondary school – was maintained by the local authority.

“We had actually sent a new action plan for this school before Ofsted came, but for some reason Ofsted did not read it and instead reported on the old one,” Jones said. “It is important to point out that the inspections were barely a week into the new school term so there obviously hadn’t been much time to make changes due to the intervening summer holiday.”

At Saltley a new executive head teacher was appointed on September 1, with the Ofsted snap inspection taking place 10 days later, on 11 September.

A DfE spokesman said: “These reports are a snapshot. They reflect the particular circumstances of the schools and the time at which the inspections took place, in some cases just a couple of days into the start of the new school year.

“The strong leadership teams we have put in place mean that change will be rapid and effective once it has had more than a few weeks to have an impact.”

The strongest criticisms by inspectors were aimed at Oldknow, where they found evidence that the primary school was riven with “split loyalties and allegiances” among staff.

“Since the last inspection, little has been achieved to address deep-seated weaknesses in governance and safeguarding,” the report states. “There is no clear focus on how to unite teams with a common purpose and some staff do not trust one another.”

The inspectors found that Oldknow’s trustees were not aware of a visit to Saudi Arabia for pupils and staff, “despite a similar trip last year receiving criticism from inspectors at the previous inspection due to failures in safeguarding. Indeed, they had been told by senior leaders that the visit had been cancelled.”

The inspectors also reported that more than 100 families had requested that their children be withdrawn from collective Christian worship at Oldknow. The schools pupils are overwhelmingly Muslim.

At Saltley, inspectors said: “Some staff segregate themselves into groups based on their religious beliefs and this has not been addressed with sufficient urgency by leaders.” At Park View: “Little has been done to discourage segregation, to encourage boys and girls to sit together in lessons”.

Russell Hobby, general secretary of the National Association of Head Teachers, said the schools needed more time to heal following a major crisis.

“Despite the seriousness of the situation in Birmingham, we must be realistic about what it is possible to achieve in a short space of time. One of the schools was inspected just after a new head teacher was appointed,” Hobby said.

“This situation needs a sustained focus and long term commitment. It is not acceptable for authorities to go back to ‘business as usual’ when the media spotlight moves on.”