Boris Johnson has claimed his comments about a British mother jailed in Iran did not make “any difference” to her case despite his words being used against her in court.

The Tory leadership frontrunner also appeared to water down pledges to deliver Brexit by October 31, to cut taxes for higher earners and to oppose a third runway at Heathrow airport.

Appearing alongside rival candidates in a BBC debate, Johnson was also forced by Sajid Javid to agree – along with all other candidates – to an investigation into Islamophobia in the party.

Johnson also apologised for causing offence with his comments about veiled Muslim women looking like “letterboxes” in a newspaper column. The piece appears likely to be included in any Islamophobia probe.

The former foreign secretary appeared on the BBC debate having avoided a larger Channel 4 event on Sunday and was forced to defend both his record and pledges made during the campaign.

Touching on his time as foreign secretary, a role he quit over Brexit in July 2018, Johnson denied that his mistaken comments about Nazanin Zaghari-Ratcliffe, a charity worker jailed in Iran on spying charges she denies, made a difference to her case.

Johnson in November 2017 wrongly stated Nazanin had been in Iran to teach journalism, when in fact she had been on holiday, and his remarks were cited as evidence against her in court four days later.

She has been in jail for more than three years and her husband Richard Ratcliffe last week told HuffPost UK that Johnson’s comments are still used against her in Iran.

Put to him by host Emily Maitlis that “words have consequences”, Johnson replied: “In that case, I didn’t think it made any difference.

“But in pointing the finger at our side what you are doing is exculpating those who are truly responsible which is the Iranian revolutionary guard, that is the reality and people should realise what this regime is up to.”

Johnson also apologised for comments he made about women who wear burkas looking like letterboxes, saying he was “sorry for the offence they have caused”, before saying his own Muslim great-grandfather would be “astonished” and “proud” that his great grandson had become foreign secretary.

On Brexit, Johnson refused to guarantee Britain would leave the EU on October 31, deal or no deal.

He said only that it was “eminently feasible” that he could hit the Halloween Brexit deadline if he became PM.

In a format where members of the public asked questions from around the UK via video link, the candidates were first urged to guarantee Brexit would happen on that date.

Johnson replied: “I think that October 31 is eminently feasible.

“If we now say that we have a deadline that is not a deadline and we allow October 31 to come and go as March came and went and April came and went I think the public will look on us with increasing mystification and we will continue haemorrhaging support.”

Johnson also watered down pledges to cut taxes for around three million higher earners by raising the 40p threshold from £50,000 to £80,000, referring to it only as an “ambition” that should be subject to “debate”.

“We should be lifting the thresholds for national insurance for the low paid but I do think it’s relevant for us all to have a debate about the thresholds for the higher rate of taxation,” he said.

“It does seem to me to be very odd that in the Conservative Party people should seriously question whether it is right to try to lift nurses, and heads of maths departments and police inspectors out of the top rate of tax.

“What we would bring forward is a package to help primarily the poorest in society by lifting the thresholds for national insurance but I think it’s very sensible to have an ambition to raise the higher rate of tax for middle income earners.”

Johnson once claimed he would lie down in front of bulldozers to prevent a third runway being build at Heathrow, but on the night refused to say he would block it.

“I continue to have grave reservations about the Heathrow runway three,” he said.

“Not just from the point of view of air quality but also noise pollution as well and I will continue to use all the instruments … to reduce CO2.

“As you know, court cases are now proceeding and as prime minister I will be following those very closely indeed.”

The next round of voting in the Tory leadership contest is on Wednesday, with Johnson in front with 126 MPs’ votes and Javid looking most vulnerable on just 33.

The final two remaining after three more rounds of MPs’ votes go to a ballot of all Tory members to choose the next leader, and PM.