Nigel Farage has claimed that Andy Burnham has given him “the biggest boost in my career” by reviving the Brexit debate, which the Reform UK leader said had reopened a “huge flank” to his party.

The prime minister’s pledges to the Labour conference and admission on Wednesday that rejoining the EU was among options the government would look at had put “put me back into the debate”, he said.

Looking tanned and relaxed before his party’s first major rally since its conference last month, Farage indicated to reporters that he was relishing a return to the playbook that he and others deployed during the 2016 referendum.

Dismissing polls showing that as much as 59% of the public favoured rejoining the EU, Farage told the Guardian: “Of course they do, until you tell them it’ll cost 25bn quid a year, until you tell him it’ll mean joining Schengen [the area of Europe that has open borders], until he tells them it will mean actually having to recommit to joining the euro.

“Remember that the leavers haven’t made their arguments since 2016. The ‘remoaners’ have made their arguments every single week. I mean, do you know what? I actually think that Burnham has made a very big political mistake here.”

Farage was speaking before a rally in the South Yorkshire city of Doncaster, the first of a series Reform is holding around Britain on the theme of what the party would do in its first 100 days of government.

While the Reform UK leader said he believed Burnham had calculated that new language on the EU might help win back voters from the Greens in big cities, Farage added: “Here in Doncaster and across the ‘red wall’ in the north and Midlands, I think he’s opened up a huge flank to us.”

To cheers from hundreds of Reform supporters who gathered inside an event space at Doncaster racecourse, Farage said: “Today I’m back on the road and today is when our general election campaign starts.”

There were even bigger cheers when Farage said he would relish – “Bring it on, I say” – the prospect of fighting Burnham in red wall areas such as Doncaster on the issue of rejoining the EU.

“He might just have given me the biggest boost in my career I’ve ever had. Thank you, Andy, if you’re watching.”

The focus of the rally – “100 days to save Britain” – had been planned before Burnham’s announcement about UK-EU relations. However, Reform sources claim that the prime minister’s intervention has energised them and that specific donors are already discussing how they can fund a rerun of the 2016 campaign.

Meanwhile, Farage strongly hinted that Reform’s internal inquiry into the donations controversy that has overshadowed the party this year would absolve two key aides and that legal action would be launched against journalists involved.

Indicating that he had already seen the report and knew its conclusions, Farage said its release was “imminent”.

“It’s been done. It’ll be out in public very soon and I think some of your co-conspirators might find themselves with one or two legal challenges,” he told a Channel 4 journalist among reporters who questioned him.

Reform was rocked on the eve of its party conference after some of Farage’s team were filmed appearing to plot to avoid electoral laws on foreign donations in an undercover investigation broadcast by Channel 4 News.

A group of investigative journalists called Verbatim, founded by the Centre for Climate Reporting, posed as a potential Reform supporter and his wealthy American father, an impermissible donor, who paid for £30,000 of polling commissioned by Reform and which benefited the party.

In Channel 4 News’s investigation, footage showed that the fake UK-based supporter also had conversations with Reform’s head of policy, James Orr, who talked about commissioning polling that would be paid for by the US-based father.

In footage of another meeting, a senior adviser to Farage, Dan Jukes, appeared to suggest to the fake UK-based supporter that his US-based father could make a substantial donation by channelling it through the son.

Jukes has denied “any wrongdoing” while Orr has said he would cooperate with the party’s internal investigation “fully”.

The Metropolitan police are carrying out a criminal investigation into Reform over allegations it broke foreign funding laws.