On Tuesday, after days of questions, the Conservatives withdrew support for two of their parliamentary candidates – Laura Saunders and Craig Williams – who are under investigation.
Russell George, a Conservative politician in the Welsh Parliament, is also facing inquiries by the regulator and has “stepped back” from his frontbench role.
Labour has disowned one of its candidates, Kevin Craig, who is under investigation after betting he would lose his bid to become an MP.
Scottish Secretary Alister Jack is not being looked into by the commission but has admitted to placing three bets on the election date.
Mr Jack, who is not standing to be an MP in the 4 July election, told the BBC that in April he placed a successful bet that the election date would fall between July and September – after losing two similar bets in March.
He said his wagers, which included two unsuccessful £5 bets and one successful £20 bet, did not breach any rules.
Asked about Mr Jack’s case, Mr Stride told BBC Radio 4’s Today programme his colleague had been “very clear” that he “hasn’t broken any of the rules or used any inside information”.
He said there needed to be a “thoughtful debate” on the general subject adding that there was “a huge difference between a politician placing a bet on what government we’ll have in 10 years’ time and someone who does something that’s more immediate – or relates for example to their own seat”.
The minister argued the focus should be on rule-breaking and that there should be “very severe consequences” if people are found to have committed wrongdoing.
Asked by Times Radio whether politicians should bet on political events, Mr Stride said: “My personal view, I would just say that people shouldn’t do it.”
Sir Keir said he thought the rules were “clear enough” and did not need to change, later adding that it was the “culture of politics” that needed to change.
“You can see why the Tories want to take this debate to should the rules change because that takes the focus away from the real issue which is the behaviour of politicians.”
He said he had acted quickly over the case of Mr Craig and accused Mr Sunak of waiting “days and days” before withdrawing support from his candidates.
The Labour leader said he had placed bets on horses but never on politics.
Sir Ed told the BBC he had placed a bet on how well his party would do in the 2010 election but lost.
He also told ITV he had bet on the 2022 by-election in North Shropshire, which his party won.
“But I think lot’s of people in politics do this. One reason why we need this review of gambling regulations is to get real clarity on what is allowed but what isn’t,” he said.