Boris Johnson has apologised for Islamophobia within the Conservative party as a Tory candidate accused the prime minister of fanning the flames of anti-Muslim prejudice.

The prime minister has faced heavy criticism for a column last year in which he used the terms “bank robber” and “letterbox” to describe Muslim women who wear a burqa and for failing to hold an independent inquiry into Islamophobia in the party.

On Wednesday, on a visit to Cornwall, asked if he apologised for the Islamophobia that has taken place in the Conservative party, he replied: “Of course, and for all the hurt and offence that has been caused – of course we do. And all that is intolerable and it’s so important as a country that we don’t allow that kind of thing and that’s why we’re going to have the independent inquiry.”

The apology was the first Johnson has made in relation to Islamophobia and came the day after Jeremy Corbyn repeatedly declined during a TV interview to say sorry for antisemitism within the Labour party, although he had previously done so.

Johnson, who agreed to an independent inquiry on Islamophobia during a televised Tory leadership debate in June, said the inquiry would be on “every manner of prejudice and discrimination”. Critics, who say anti-Muslim prejudice is rife within the party and requires specific scrutiny, insist that is not good enough.

Johnson’s apology came after Parvez Akhtar, the Conservative candidate for Luton South, called on the prime minister to unequivocally apologise for comments he made about Muslim women in the Telegraph last year and hold an independent inquiry into Islamophobia within the party.

“Whatever the intent of the column the effect has has been to reinforce the widely held view that the Conservative party has a blind spot when it comes to Muslims,” said Akhtar. “This view is further exacerbated by the fact that the prime minister refuses to apologise for those comments and hold an independent inquiry into Islamophobia despite committing to it on live television.”

Akhtar said he had twice personally experienced anti-Muslim hatred aimed at him within the party since joining in 2005, but had not left because he felt the only way to effect change was from within.

He said he continued to believe that a Conservative government was best for the country, including Muslim communities, but gave the example of the former Labour MP for Luton South, Gavin Shuker, who highlighted antisemitism within his party.

Akhtar said: “I can no longer remain silent as I would be complicit in the blatant discrimination which exists not only within the party towards individuals but also when it comes to the policy agenda.”

Johnson was widely criticised by senior Tories after his remarks in the Telegraph, with demands for an apology, including from the then party chairman, Brandon Lewis. The Tell Mama monitoring group said they had led to a 375% increase in anti-Muslim attacks and incidents of abuse. Nevertheless, Johnson has consistently refused to apologise.

The former Tory chair, Sayeeda Warsi, who has campaigned against Islamophobia for years, applauded Akhtar’s stand and said Johnson’s apology was “a good start”.

She told BBC Radio 4’s World at One programme: “I’m pleased that finally we are starting to get to a point where hopefully we can start to acknowledge the extent of this issue.”

Shuker, now an independent candidate, said: “I commend Parvez on his principled decision to call out Islamophobia in the Conservative party. It’s distressing that both legacy parties have failed so badly to deal with the institutional racism in their ranks.”

In response to Johnson’s apology, Akhtar called the prime minister’s comments “very generous”, but added: “While I accept his apology for hurt and offence caused by Islamophobia within the party, I think specifically his comments were the views that were hurtful even if that was not his intent and I think he should apologise for those as well.”

He maintained that an independent inquiry into Islamophobia was still necessary to ascertain the scale of the problem.