“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 at work, food standards and all the rest of it.”
It was not immediately obvious from the comments whether he was talking about divergence in the specific areas he mentioned, or in general.
His remarks were livestreamed but first reported by Sky News on Thursday, prompting claims from Tory ministers that Sir Keir was changing his stance on Brexit.
Housing Secretary Michael Gove said they revealed “the real Keir Starmer” and that he wanted to “re-run the Brexit agonies of the past”.
Foreign Secretary James Cleverly said it showed the Labour leader “wants to rejoin the EU in all but name”.
A Labour spokesperson rejected this, insisting the UK would not be going back into the EU “in any form”, and suggested Sir Keir’s comments were limited to the areas of food, environmental and labour standards.
Asked about the Tory criticism of his comments during a visit to the London Stock Exchange, Sir Keir told broadcasters: “I have repeatedly said that there’s no case for going back into the EU and that includes the single market and the customs union.”
Countries in the EU single market apply many common rules and standards, while countries in the customs union share the same customs regulations.
Sir Keir said: “We will not be a rule-taker. The rules and laws of this country will be made in Parliament according to the national interest.
“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.”
He said this was no “surprise” and that Labour had been “consistent” on this for years.
“Incidentally, this is also government policy,” he added.
Sir Keir, a former Remain supporter, unsuccessfully campaigned for a second EU referendum as Labour’s shadow Brexit secretary under Jeremy Corbyn.
Since becoming Labour leader he has been keen to win back Brexit-supporting voters and has been reluctant to raise the prospect of closer ties with the EU.
However, he has recently raised questions over the relationship a future Labour government could have with the bloc, saying his party would seek a “much better” Brexit trade deal.
He said the deal, originally negotiated by Boris Johnson and up for review in 2025, was “too thin” and that he would improve it, although he did not specify how.
Labour says it would negotiate a new agreement on the movement on animal products, and recently said it wanted a new deal with the EU to stop migrant crossings over the English Channel.
Lib Dem leader Sir Ed Davey has also said rejoining the EU is currently “off the table”.
The party, which was defined by its “Stop Brexit” stance four years, now wants to focus on domestic issues as it seeks the support of voters who backed Leave, as well as those who wanted to stay in the EU.