A promised independent inquiry into Islamophobia in the Conservative party has been downgraded to a “general investigation” into all types of prejudice, Boris Johnson has said, going back on what was seemingly agreed in a recent BBC debate.

The move was condemned by the Muslim Council of Britain (MCB), which said it demonstrated an “unwillingness to deal with bigotry seriously”, while Labour said Johnson had “broken his promise in less than two weeks”.

In an interview with the ConservativeHome website, the Tory leadership frontrunner said he had agreed with Sajid Javid, the home secretary, who pushed for the Islamophobia inquiry, that it should instead have a broader focus.

The idea was raised by Javid during a BBC leadership debate involving the candidates still in the race at the time – the others being Johnson, Jeremy Hunt, Michael Gove and Rory Stewart.

Asked if he believed such an inquiry should be held, Javid said: “Yes I would – do you all agree, guys? Shall we have an external investigation in the Conservative party into Islamophobia?” The other candidates all seemingly agreed, with none raising any objections.

But in the ConservativeHome interview, when asked about the plan, Johnson said: “Well, I took it up with Saj afterwards and he said that actually, if I understand it correctly, what we’ve committed to is a general investigation into all types of prejudice and discrimination, including antisemitism.”

Asked if this would be an independent investigation, Johnson replied: “Yup.” He added: “So yes, we’ll have to study exactly what Saj has in mind, but it sounded like a sensible idea when he mentioned it.”

There was no response from representatives of Javid when asked to confirm that he had agreed to this plan.

The apparent downgrading of the inquiry will disappoint anti-Islamophobia campaigners, who have repeatedly called for the Conservatives to tackle the issue.

A poll of Tory members earlier this week found nearly half would prefer not to have a Muslim prime minister.

The survey, carried out by YouGov for the anti-racism group Hope Not Hate, also found more than two-thirds of Tory members believe the myth that parts of the UK are under sharia law, and 45% think some areas are not safe for non-Muslims.

Half the party’s members think Islamophobia is a big issue, but only 8% believe it is a problem within the party, the survey found, while 40% of members wanted to see fewer Muslims in the UK.

An MCB spokesman said: “We are disappointed to see that Mr Johnson has apparently reneged on his promise for an independent inquiry into Islamophobia in the Conservative party.

“It has become all too apparent that the Conservatives have a problem with Islamophobia, as evidenced this week with a damning poll revealing how rank-and-file Conservative party members hold conspiratorial views on Muslims.

“Rowing back on the promise only demonstrates further unwillingness to deal with bigotry seriously. We expect nothing less than a full and independent inquiry into Islamophobia.”

Naz Shah, the shadow equalities minister, said: “Boris Johnson has broken his promise in less than two weeks. Anything short of a full, independent inquiry into Islamophobia and racism in the Conservative party will be an insult to Muslim communities, and will compound the hurt and anguish that is already being felt.”