Ukip’s campaign in Stoke-on-Trent Central is insufficiently organised to convert the city’s Brexit majority into support at the ballot box, rivals say.

The claim came as the party’s leader and candidate for next week’s crunch byelection, Paul Nuttall, was forced to move house amid fears for his safety. He has also had to deny allegations that he lied about being present at the Hillsborough disaster in 1989.

Ukip is the bookmakers’ favourite to take the seat following the resignation of the Labour MP Tristram Hunt. A handful of polls commissioned by Eurosceptic groups have put Nuttall well ahead of the Labour candidate, Gareth Snell.

Victory in the city, where 70% voted to leave the EU, would lend weight to fears that Labour is on the brink of meltdown in its provincial heartlands. A Labour hold would raise serious doubts over Ukip’s post-Brexit appeal, although Nuttall says the seat is 72nd on the party’s target list.

However, Chris Lovell, the Lib Dems’ campaign manager, said Ukip was likely to underperform expectations. “Ukip aren’t going to win it, I can be definite on that,” he said.

“Ukip talk themselves up but don’t know how to fight elections. Our ground game is miles better than theirs, as is Labour’s. From our data, I’d be relatively confident that Ukip aren’t going to win.”

Turnout for the EU referendum was 65.7%, compared with just 49.9% – the lowest of any seat in the country – in the 2015 general election. Recent polls have consistently shown that Remain voters are more likely to turn out.

In Stoke on Friday, Nuttall’s campaign manager, Richard Wright, said speculation that the Conservatives had deliberately pulled back to allow Ukip a clear run was misplaced. Although some Tory supporters had pledged to lend Nuttall their votes on 23 February, Wright said the Tories, who finished just 33 votes behind Ukip in 2015, had a “hard core” of local support who were proving difficult to woo.

Merseyside-born Nuttall’s bid to become an MP is already the subject of a police complaint into allegations of electoral fraud, after the house he named as his home address on his nomination papers appeared to be empty at the time. He was plunged into further controversy when he was forced to deny allegations that he had lied about being present at the Hillsborough tragedy, when 96 Liverpool fans died.

Liverpool’s elected mayor, Joe Anderson, said Nuttall should withdraw if his claims were incorrect. “If it is true that he was at Hillsborough, then it is extremely disappointing that during many years of pain and anguish for the families he never once used his position nationally and internationally to stand up for people from his own community and join the fight for justice,” he said.

“If it’s not true then he needs to withdraw a campaign built on lies. Either way, it’s clear the people of Stoke deserve better than Ukip or Paul Nuttall.”

Ukip issued a statement that said that any claim Nuttall was not at Hillsborough was “totally false and highly defamatory”. The party added: “Paul was indeed at Hillsborough. He attended the match with his father and other family members. For political opponents to suggest otherwise and for leftwing media organisations to promote such claims constitutes a new low for the Labour party and its associates.”

The Lib Dems, who fell from second to fifth at the 2015 general election, believe cardiologist Zulfiqar Ali could make a breakthrough as the only candidate opposed to a hard Brexit in the aftermath of last Wednesday’s divisive parliamentary vote on article 50, pointing to unlikely victories in recent council byelections in Sunderland and Rotherham.

Local activists believe that if Labour wins, they can beat Ukip into third. Campaigners say canvass returns from areas predominantly populated by public sector workers show large numbers of Labour voters lending their support to Ali, a Pakistani immigrant who is banking on the support of the seat’s sizeable Kashmiri population.

Asked whether he was worried by the prospect of a late surge in Lib Dem support in the wake of Labour’s controversial vote in favour of article 50, the party’s candidate Gareth Snell said voters should “think about who you are going to get elected and use your vote wisely”. However, in a blow to lingering hopes of an informal progressive alliance between Labour, the Lib Dems and Greens, both Tim Farron and Caroline Lucas urged local people to back their own candidates and attacked Labour’s stance on Europe.

Labour activists say their support is holding up and Snell played down the significance of the European question. “Of all the things that keep me awake at night, the Liberal Democrats aren’t one of them. This is a race between me, the Tories and Ukip … I think a Paul Nuttall victory would be a disaster for the Potteries.”

Patrick Maguire is winner of the 2016 Anthony Howard award for young journalists. Applications are now open for this year’s award. The prize is £25,000 and successive fellowships at the Times, the Observer and the New Statesman. For details go to anthonyhowardaward.org.uk