The main representative group for the British Jewish community has warned the Conservatives they should not avoid “difficult questions” over prejudice in the party after a promised inquiry into Islamophobia has instead become a broader review of discrimination complaints.

Marie van der Zyl, the president of the Board of Deputies of British Jews, said it was important that in widening the inquiry into all forms of prejudice the Tories did not “make the same mistakes” as Labour did over antisemitism.

The Conservatives are facing considerable pressure over anti-Muslim sentiment in the party, not least due to comments by Boris Johnson, who has refused to apologise for writing an article comparing Muslim women in burqas to “letterboxes” and “bank robbers”.

In the election campaign, it emerged that more than two dozen sitting and former Conservative councillors had been exposed for posting Islamophobic and racist material on social media.

During the Tory leadership campaign in June, Sajid Javid sought the backing of Johnson and other candidates for an inquiry into Islamophobia in the party during a live TV debate, which they all agreed to.

However, the inquiry, announced on Tuesday, will instead examine the party’s handling of complaints of any form of discrimination and prejudice. It is headed by the former equality and human rights commissioner Swaran Singh, professor of social and community psychiatry at the University of Warwick.

The Muslim Council of Britain said the approach risked being seen as one of “denial, dismissal and deceit” towards Islamophobia.

In the Board of Deputies’ statement, Van der Zyl said: “As the Conservatives embark on an inquiry designed to strengthen its approach to racism – particularly including Islamophobia – and reassure British Muslims and other communities about its approach, it must avoid making the same mistakes as the Labour party over antisemitism.

“It should seek to ensure the approach is genuine, asks the difficult questions, and show a willingness to change if things have gone wrong in the past.

“It should be said that in our own dealings with the Conservative party over incidents of antisemitism and other forms of racism, we have found it to be responsive and swift. But it seems that other minority groups have not all had the same experience and this should be addressed. Where we can play a constructive role we are certainly willing to do so.”