The Conservatives have been accused of ignoring systematic Islamophobia in their ranks after Boris Johnson broke his promise to hold an inquiry specifically into the issue and announced a broad-brush review of how the party handles discrimination complaints instead.

The Muslim Council of Britain expressed concern at the move on Tuesday, saying it suspected that broadening the remit was designed to bury the real problem.

“This appointment is at risk of being seen in the same light as the Conservative party’s customary approach to Islamophobia, that of denial, dismissal and deceit,” said its general secretary, Harun Khan.

“We were promised an independent inquiry into Islamophobia specifically. Now we have a review that aims to broaden the scope to examine discrimination more generally. A laudable aim if it were not for the fact that the Conservative party is afflicted with a particular type of bigotry that it refuses to countenance.”

The prime minister, who has himself publicly ridiculed Muslim women who wear the burqa, indicated that he would renege on his pledge to hold the more focused inquiry within a fortnight of making the vow live on television as he sought the Conservative leadership this summer.

Johnson faced staunch criticism as the plan was quickly watered down and the Tories have opened numerous investigations into allegations of Islamophobic behaviour by party figures in recent months.

While he has declined to apologise for the comments he has made in newspaper articles, Johnson has said sorry in more general terms for “all the hurt and offence that has been caused” by Islamophobia within the Tory party during the general election campaign.

On Tuesday, five days after the vote that handed the party a solid Commons majority, the Conservatives appointed the former equality and human rights commissioner, Prof Swaran Singh, to lead the independent review into the party’s handling of complaints of any form of discrimination and prejudice.

The Tories said the review run by Singh, a professor of social and community psychiatry at the University of Warwick, would look at how they could improve their processes, to ensure “any instances are isolated, and that there are robust processes in place to stamp them out as and when they occur”.

The party’s chairman, James Cleverly, said it was committed to stamping out “unacceptable abuse”. He added: “The Conservative party has always worked to act swiftly when allegations have been put to us and there are a wide range of sanctions to challenge and change behaviour.

“The Conservative party will never stand by when it comes to prejudice and discrimination of any kind and it is right to hold an independent review, so we can stamp out unacceptable abuse that is not fit for public life.”

The Tories have been heavily criticised by their former chair, Sayeeda Warsi, who has long campaigned against Islamophobia in the party.