Sir Keir Starmer has insisted he will not allow the UK to become a “rule-taker” after his comments suggesting he did not want to diverge from EU rules sparked criticism.

The Labour leader immediately rejected suggestions from the Conservatives that he wanted to take the UK back into the EU, telling reporters: “There is no case for going back into the EU, and that includes the single market and customs union.”

“Equally, we will not be a rule-taker,” he continued. “The rules and laws of this country will be made in parliament according to the national interest.”

However, he added: “But that does not mean that a Labour government wants to lower standards on food, wants to lower standards on people’s rights at work.

“The Labour Party has been completely consistent on those issues for many many years – there is no surprise here. Incidentally, this is also government policy.”

His remarks come after the Labour leader declared “we don’t want to diverge” from EU rules in footage of a conference of centre-left leaders in Canada seen by Sky News.

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Sir Keir argued Britain’s relationship with the EU could be much stronger, while still remaining outside the bloc and outside the single market, “the more we share a future together”.

The comments have triggered a fresh discussion over how Labour would approach Brexit, with the Tories immediately seizing the opportunity to accuse Sir Keir of wanting to take the UK back into the EU.

Levelling Up Secretary Michael Gove said the remarks had shown “the real Keir Starmer” and claimed the Labour leader wanted to “return us into the EU” and “re-run the Brexit agonies of the past”.

Earlier on Friday, a Labour frontbencher told Sky News there would “clearly be ways” in which the UK does diverge from the EU, including through individual trade deals.

James Murray, Labour’s shadow financial secretary to the Treasury, said his party had been “very clear throughout” about any “red lines” there would be with the EU post-Brexit.

He said “we don’t want to be in the single market, we don’t want to be in a customs union, we don’t want to bring back freedom of movement – but we do want a better trading relationship”.

Mr Murray hit back at the criticism from the Conservatives and said they had “no plan to make Brexit work”.

Asked how the UK could maximise the advantage of Brexit if it did not diverge from EU rules, Mr Murray told Sky News: “Well, there will clearly be ways in which we do diverge in terms of striking our own trade deals with other countries and so on.

“But the conversation that we’re having today is focused on UK standards and I think what Keir was saying is we have no interest in weakening or watering down UK standards when it comes to things like food standards, consumer protection, workers rights and so on.”

His remarks were echoed by London mayor Sadiq Khan, who said Sir Keir is “right to say, ‘look, the current deal we have with the European Union has got big problems in it’. Some characterise it – I would – as an extreme, hard Brexit deal.”

He said it’s “right” that Sir Keir would seek to “look into having a better deal” when the current deal, negotiated by Boris Johnson, is up for review in 2025.

Mr Murray said there would still be areas where a Labour government would diverge from Brussels, for example by striking trade deals around the world.

He added: “All we’re seeing under the Conservatives is extra red tape on businesses, which means that it’s impacting on economic growth, which means it’s deepening the cost-of-living crisis.”

Sir Keir’s statement was made just days after he was forced to shut down speculation he might join an EU quota system on migrants after he said he would talk to the bloc about a returns deal – prompting the Conservatives to brand him “Mr Open Borders”.

His statement on Saturday evening came in response to a question from John McTernan, a former aide to Sir Tony Blair, at a conference for progressive leaders in Montreal.

Sir Keir said: “Most of the conflict with the UK being outside of the EU arises in so far as the UK wants to diverge and do different things to the rest of our EU partners.

“Obviously the more we share values, the more we share a future together, the less the conflict. And actually different ways of solving problems become available.

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“Actually we don’t want to diverge, we don’t want to lower standards, we don’t want to rip up environmental standards, working standards for people that work, food standards and all the rest of it.

“So suddenly, you’re in a space where, notwithstanding the obvious fact that we’re outside the EU and not in the [European Economic Area], there’s a lot more common ground than you might think.”

A Labour spokesperson said following the remarks that the UK had “left the European Union and we’re not going back in any form”.

“Any decisions on what standards we follow will be made in the UK parliament,” they added.

“The Tories have not used Brexit to diverge on food, environmental or labour standards and if they have a plan to do so then they should come clean with people.”