The Church of England has indicated it will comply with new rules that will compel all schools including faith schools actively to promote fundamental British values, including tolerance for other faiths and lifestyles.

Nicky Morgan, the education secretary, revealed at the weekend that guidance on new rules introduced in the wake of the "Trojan Horse" scandal in Birmingham will be issued to private schools, academies and free schools this week.

Inspectors will be able to take action against schools that do not conform to the Equality Act, which encourages respect for lesbian, gay and transgender people along with other religions and races.

Although the Trojan Horse affair, when a number of individuals attempted to introduce extremist Islamist concepts, did not concern faith schools, Ofsted made snap inspections of 40 schools including Christian and Jewish faith schools in its wake.

Some of the schools inspected say they have been penalised for not celebrating enough festivals of other faiths, not giving children sex education lessons, not teaching them to be tolerant of homosexuality and not inviting faith leaders to speak at assemblies, the Sunday Times reported.

However the Church of England today reinforced its commitment to encouraging community cohesion through its 4,700 schools.

One in four primary schools and one in 16 secondary schools in England are Church of England schools, educating nearly a million pupils.

Rev Nigel Genders, the Church's chief education officer, said: "Church of England schools have always been committed to providing a high quality education for all young people, of all faiths and none.

"Clearly this must include rigorous and challenging religious education to equip young people with the knowledge and understanding of a range of faith systems. We were delighted that the government recently acted to support us in doing this by providing bursaries for those training to teach RE.

"We take just as seriously our role to ensure that the rights of LGBT young people are included in the curriculum and that they feel welcome in our schools. That is why we developed a resource to help all schools combat homophobic bullying. We are delighted that the Secretary of State is now funding a major project on this issue.

"All our schools teach about same sex marriage being the law, but we also feel it is important to reflect that there are different views on marriage, including that of the Church, and we would expect all schools to do the same."

Morgan, a committed Christian who has changed her mind and now supports same-sex marriage, told the Sunday Times it was "crucial" that Christian and Jewish schools, as well as Muslim ones, followed the new rules.

She said: "Schools should broaden horizons not close minds ... and should encourage pupils to respect other people, even if they do not agree with them. I should have thought this is a principle with which the vast majority of people would agree. All schools, of whatever type, have a duty to protect young people and to ensure they leave school fully prepared for life in modern Britain."

She added: "These values – democracy, the rule of law, individual liberty, and mutual respect and tolerance of those with different faiths and beliefs – are not new. The requirement to 'actively promote' them is designed to reinforce the importance this government attaches to these values."

A Jewish school for girls in Salford last week was placed in special measures after Ofsted inspectors said there were "major gaps" in students' spiritual, moral, social and cultural development and ruled that students are not provided with sufficient opportunities to learn about or understand people of other faiths or cultures and did not prepare students adequately for life in modern Britain.

Last week the govrnment announced a £2 million package for schools to help them tackle homophobic bullying.

The cash will be given to charitable and not-for-profit organisations who can come up with "creative ideas" to stamp out the bullying.

Jo Swinson, Minister for Women and Equalities, said: "Young people should grow up feeling safe expressing who they are, and we know that homophobic bullying stands in the way of this.

"We know the damage bullies can cause to young people's self-esteem and educational attainment. There should be absolutely no excuse for this taking place in our schools."

The law was changed in 2012 to strengthen the powers teachers have to enforce discipline and good behaviour. Schools have been given advice on their legal duties and powers, and other resources to help them put an end to bullying.