Birmingham city council is investigating an alleged plot to oust headteachers in the city, replacing them with people who will run their schools on "strict Islamic principles".

A letter, passed to the Birmingham city council late last year as well as various schools in the area, outlines a plan dubbed "Operation Trojan Horse" and claims up to four schools in the city have already been "taken over".

The West Midlands counter-terrorism unit said it was aware of the letter and was working with the council to identify whether a police investigation is warranted.

A copy of the undated and unsigned letter, seen by the Guardian, offers a five-step plan to take over schools in communities with large Muslim populations with the help of what it calls "hardline" parents who follow the strict Salafi branch of Islam. However one of the alleged plotters, Tahir Alam – a former chair of the education committee of the Muslim Council of Britain – told the Guardian on Friday evening that the letter was "a malicious fabrication and completely untrue".

The alleged plan suggests "turning" the parents against the head and leadership team by telling them "that the school is corrupting their children with sex education, teaching about homosexuals, making their children pray Christian prayers and mixed swimming and sports".

Apparently written from one Islamic fundamentalist to another, it says that the "operation" is a "long-term plan and one which we are sure will lead to great success in taking over a number of schools and ensuring they are run on strict Islamic principles".

The author(s) claim they have "tried and tested" the plan in Birmingham and suggest their methods can be replicated in Bradford by forcing heads out of office and then lobbying to turn schools into academies.

They wrote: "We have caused a great amount of organised disruption in Birmingham and as a result now have our own academies and are on the way to getting rid of more headteachers and taking over their schools. Whilst sometimes the practices we use may not seem the correct way to do things you must remember that this is say 'jihad' and as such using all measures possible to win the war is acceptable."

The letter names four Birmingham schools where they have already had "success": Adderley Primary, Saltley School, Park View School and Regents Park Community Primary School.

Last October headteacher Tina Ireland resigned from Regents Park after an investigation into the school's outstanding SATs results. The letter's authors claim they "planted the seed of her cheating in order to get the results she has".

Saltley's headteacher resigned last year after a critical Ofsted report. Inspectors said there was a "dysfunctional" relationship between head teacher Balwant Bains and governors which was hindering the school.

On Friday, Jawed Iqbal, chair of governors at Adderley, said on Friday he had reported the matter to West Midlands police, who had "confirmed they will be launching an investigation".

The Operation Trojan Horse letter accuses Adderley's head of being "not a good Muslim" who was "not open to our suggestions of adhering to strict Muslim guidelines".

This week Ofsted inspectors launched a surprise inspection at Park View Academy in Alum Rock, where it has previously been reported one staff member has complained non-Muslim employees are being discriminated against. It was also claimed the school was attempting to introduce Islamic studies to the curriculum.

Superintendent Sue Southern, the head of West Midlands' prevent and protect counter-terrorism Unit, said: "In December 2013 Birmingham city council brought the content of a letter they were investigating to the attention of West Midlands counter-terrorism unit requesting we make an assessment of whether any criminal offences had been committed.

"The assessment at that time and [it] remains the case today is that the allegations in the letter were for further investigation by Birmingham city council and [the] Department for Education and were not a matter for the police.

"The city council has continued to keep us updated on their inquiry in the event that any findings either warrant police investigation or impact on our joint delivery of [the] Prevent [programme] across the city.''

A Department for Education spokesperson said: "We are aware of the serious allegations made in relation to some schools in the Birmingham area, including Park View, which are now being investigated by Birmingham city council and West Midlands police.

"We will not hesitate to take firm action if necessary. It would be inappropriate to comment further at this stage."

A Birmingham city council spokesperson said: "We have received letters making allegations in relation to some schools in the Birmingham area. The city council is continuing to investigate these allegations and therefore cannot comment further."

The alleged plot was condemned by Inayat Bunglawala, chair of Muslims4UK, a group which aims to promote active Muslim engagement in British society. He said: "The contents of this document are very disturbing. On the face of it this would appear to be part of a radical agenda by a tiny yet highly committed group of activists to impose their very conservative and bleak vision of Islamic teachings in our schools by fomenting division and distrust against the existing school leadership. It constitutes highly objectionable and unethical behaviour."