The Ukip leader, Paul Nuttall, has said he spent three hours on Monday giving an official witness statement to the police investigation into the Hillsborough disaster.

Nuttall said he accepted he had been wrong to allow a press release in his name to say he had lost “close personal friends” in the crush at the football ground, which killed 96 Liverpool fans, but insisted he had been present at the match.

He told BBC Radio 5 Live: “It is part of a wider smear campaign started last Friday whereby there was a claim I wasn’t at the Hillsborough disaster, even though I provided witness statements I was there and spent three hours yesterday morning at Operation Resolve giving a witness statement.”

Operation Resolve is the criminal investigation into the 1989 disaster, examining evidence of wilful neglect by police and officials. It has so far sent to the Crown Prosecution Service possible charges of gross negligence manslaughter, perverting the course of justice, misconduct in public office and offences for breaches of the Safety of Sports Grounds Act 1975 and health and safety laws.

Nuttall said he would not resign if he lost the Stoke Central byelection on Thursday. He is fighting Labour’s Gareth Snell for the seat, which Labour holds by a majority of 5,179, but his campaign has been dogged by the controversy over his Hillsborough comments.

The Ukip donor Arron Banks added fuel to the row by saying he was “sick to death” of hearing about the disaster. Over the weekend, two Ukip chairmen in Merseyside resigned in protest at the “crass insensitivity” of the party’s handling of the controversy.

Nuttall said he wanted to put his comments “in perspective”, insisting he had been present at the disaster, despite surprise expressed in comments to the Guardian by a former schoolmate and teacher.

One of his former teachers, a Roman Catholic priest, told the Guardian that the school believed it had been aware of the identities of every boy who had been at Hillsborough, in order to help them through a difficult period, but Nuttall was not among them.

Nuttall, who admitted on Liverpool’s Radio City Talk that he did not lose “close personal friends”, contrary to quotes in his name on his website, said the mistake “wasn’t crass, maybe Arron Banks was, but I made a genuine error”.

“Of course I’ll apologise to the people of Liverpool, I’ll apologise to everyone for not checking what went up on my website. It’s my fault,” he said. “I haven’t spoken to him. Arron Banks isn’t a member of Ukip so I can’t kick him out of an organisation he isn’t a member of. But I have publicly condemned it. He’s not a member, he has given money in the past.”

Nuttall said he would not resign if his campaign foundered in Stoke. “It will only be 12 weeks into my leadership at the end of this byelection. What we have got here is a long-term project going forward,” he said.

Snell has also suffered embarrassment during the campaign after offensive Twitter comments about guests on the TV programme Loose Women were unearthed, as well as criticism of the Labour leader, Jeremy Corbyn, as an “IRA-supporting friend of Hamas”.

At the Radio 5 Live hustings, Snell said he wanted to apologise again. “I have apologised to my wife and my grandmother and my daughter because those aren’t words I would like them to have to face,” he said. “So if I can take the opportunity to apologise, I will do.”

Snell said his criticism of Corbyn was because of a “very fractious summer in our party” when Owen Smith challenged Corbyn for the leadership. “We spent a lot of time arguing amongst ourselves,” he said. “Things got very heated and things were said. The comments that I made were to point out that we were getting to a point of hyperbole in our party that was damaging us publicly.

“But since then I’ve met with Jeremy. He’s been to the constituency three times. He’s been campaigning with us. He’s been on the doorstep. And every time he spoke to somebody, they’ve been glad to talk to him.”

Police released a statement saying that the Ukip leader had spoken to investigators. It said: “Operation Resolve can confirm that yesterday we spoke to Mr Nuttall and have taken a witness statement from him. Our role is to investigate the causes of the Hillsborough disaster and to establish whether any individual or organisation is criminally culpable and, in that context, Mr Nuttall met criteria for taking a statement. It would be inappropriate for us to comment any further.”

Prof Phil Scraton, the criminologist who spearheaded the campaign to overturn the official cover-up over the cause of the disaster, questioned why Nuttall had not come forward when the campaign was headquartered at the college where he was a mature student.

Writing in the Liverpool Echo, Scraton said that the Hillsborough Project, of which he was the director, produced two substantial reports and a book, and also assisted with a drama-documentary while it was based at what is now Edge Hill University.

“The coverage, especially in the north-west, was extensive. We hosted meetings with families and survivors at Edge Hill. Paul Nuttall studied history at the college. Our centre was in the heart of the campus. We must have passed each other on numerous occasions – on the pavements, corridors, coffee bar and so on. He would have walked past our centre many times.

“During that period, given the massive publicity our work received, Paul Nuttall could not have failed to know about the project, its work with the bereaved and survivors. Yet he never approached us, never shared his experiences.

“I understand fully there were many people who were, and have remained, unable to talk about what they witnessed on the day. What is not so readily explained is why Paul Nuttall did not drop by for even a confidential conversation, why he held back on disclosure until the Hillsborough Independent Panel was in session and why he chose national television as the forum to break his silence?

“These are questions of timing and context that, alongside the questions regarding the details of his experiences on the day, require explanation.”