Rishi Sunak and Keir Starmer have clashed over their responses to the Westminster gambling scandal, as it emerged the Metropolitan police is to widen its role in the investigation into bets placed on the general election.

In the last head-to-head debate before voters go to the polls, the Labour leader launched a fierce attack on the culture at the top of the Conservative party, saying it showed the “wrong instinct” to place bets on the future of the country – likening it to the cavalier attitude to Covid rules.

In the angry exchanges, Sunak repeatedly urged the country not to “surrender” to Labour’s plans on tax and migration and said the general election should not be decided purely based on frustration with the Conservatives.

“I understand why you’re frustrated with our party, with me, I get it. But this is not a byelection, it’s a choice with profound consequences for you and our country,” he said. “And before you make that choice, think what a Labour government would mean.

“Can you afford to pay at least £2,000 more in tax?… And if you’re not certain about Labour, don’t surrender to them, don’t vote for any other party, vote Conservative.”

In response, the Labour leader said of the claim that Labour would raise taxes by £2,000 a household: “That is a lie [on tax], he’s been told not to repeat that lie and he’s just done it.”

The UK’s statistics watchdog has previously issued the Conservatives with a warning over the claim, saying they had failed to make clear how the figures were calculated.

Five Conservative politicians and staffers have now been suspended for allegedly betting on the election date. Labour was drawn into the gambling row on Tuesday after being forced to suspend one of his own candidates for betting he would not win the seat he was contesting.

Starmer said he had suspended his candidate, Kevin Craig, “within minutes” – comparing his actions with Sunak, who took days to make the decision. “I think that in the last 14 years politics has become too much about self entitlement, and MPs thinking about what they could get for themselves,” he said.

“The instinct of these people to think the first thing they should do is try to make money, that was the wrong instinct, and we have to change that.”

He said Sunak had “delayed and delayed and delayed” and had been “bullied into” taking action. “My candidates know I have the highest standards. They have seen by my actions the consequences,” he said.

It comes as the Met police confirmed it was investigating a “small number of cases” related to the Westminster gambling row to “assess whether the alleged offending goes beyond Gambling Act offences to include others, such as misconduct in public office”.

A Met police spokesperson said it would announce more on its investigation on Thursday. “The Met is not taking over the investigation into bets on the timing of the General Election. The Gambling Commission will continue to lead the investigation into cases where the alleged offending is limited to breaches of the Gambling Act only,” it said.

The Guardian uncovered the gambling scandal two weeks ago, revealing that Craig Williams was the subject of an investigation by the watchdog for betting that the election would be in July, three days before it was called.

The watchdog is also examining bets allegedly placed by Tony Lee, the Conservative party’s campaigns director and his wife, Laura Saunders, the Tory candidate in Bristol North West, as well as Nick Mason, the Tories’ chief data officer.

The Guardian also revealed that Russell George, a Tory member of the Welsh parliament who represents the same constituency as Craig Williams, is part of the commission’s inquiry.

Six of the Met’s own officers have been caught up in the scandal so far, with one, a protection officer for the prime minister, under investigation for misconduct in public office having allegedly placed five bets on the election date.

Labour suspended the Central Suffolk and North Ipswich candidate Kevin Craig and said it would now return £100,000 he had donated to the party under Starmer’s leadership, while the shadow health secretary, Wes Streeting, would give back £13,000 donated for staffing costs.

In the second and final debate between the two leaders, hosted by the BBC, they clashed over the economy, immigration and their prime ministerial qualities. Loud protests were heard from outside the building in Nottingham during the exchanges.

Starmer said Sunak would be “Liz Truss Mark II” and that the same damage would follow. “He’s now openly admitted the damage that the Conservatives have done to this country and then is now saying – vote for me.”

He also drew applause from the audience for challenging Sunak on the cost of living, saying: “If you listened to people across the country more often you might not be so much out of touch.”

Starmer accused Sunak of using trans people as “a political football to divide people”, though both said they would protect women’s rights to single sex spaces.

The Labour leader drew whoops of applause when he said that he believed trans people should be treated with “dignity and respect … if you don’t, we end up with the prime minister of the United Kingdom standing in parliament making an anti-trans joke in front of the mother of a murdered trans teenager.”

Sunak replied: “That’s not what I did. I was pointing out that you’ve changed your mind on this question multiple times.”

But Sunak landed blows on Starmer earlier in the debate by questioning his plans on illegal migration, saying his plans for return agreements for migrants were “nonsensical” when it came to countries such as Iran and Afghanistan.

“He says he’s going to sit down with people. Are you going to sit down with the Iranian ayatollahs? Are you going to do a deal with the Taliban? It’s completely nonsensical what you are saying. You are taking people for fools,” Sunak said.

The Labour leader said that Sunak’s plan to deport people to Rwanda was also not having any deterrent effect.

“At the moment they are not being processed … there are tens of thousands of people sitting in hotels and you haven’t processed their claims. At the moment 100% of them are effectively being granted asylum … and because they aren’t being processed, they can’t be returned to where they come from,” he said.

The prime minister said that Starmer also had no plan for how he would deal with those asylum seekers currently in limbo. “If Keir Starmer becomes prime minister, all those illegal migrants will be out our streets, and that is a choice for you,” he said.

“Do not surrender to the Labour party the control of our borders. If Labour wins, the people smugglers are going to need a bigger boat.”