The party’s leader has pledged to begin talks with Brussels in 2025 if he makes it to Number 10, saying he “owes it to his children”.
Sir Keir met with Canadian prime minister Justin Trudeau over the weekend as part of a mini-summit of centre-left leaning politicians in Montreal. He is set to meet French president Emmanuel Macron later this week as part of a flurry of meetings before conference season.
Labour have long been critical of the trade and cooperation agreement drawn up under Boris Johnson’s administration.
"Almost everyone recognises the deal Johnson struck is not a good deal - it’s far too thin,” Sir Keir told the Financial Times on Sunday.
"As we go into 2025 we will attempt to get a much better deal for the UK."
Downing Street said on Monday Britain’s trade deal with the EU does not need to be renegotiated, describing it as “the world's largest zero tariffs zero quota deal”.
Rishi Sunak’s official spokesman said: “We are not looking to relitigate the past or reopen it in any way, shape or form.
“There is a set statutory review period, but beyond that we are very much focused on maximising the opportunities it presents for the public.”
Labour has a 15 to 20 per cent lead over the Conservatives and Sir Keir wants to position himself as a prime minister in waiting ahead of an election, likely to be next year.
Sir Keir has ruled out rejoining the customs union or single market, but the leader said he was confident a better deal could be secured from Brussels.
He said he does think “we can have a closer trading relationship as well,” and that “is subject to further discussion”.
"We have to make it work,” he continued. “That’s not a question of going back in. But I refuse to accept that we can’t make it work. I think about those future generations when I say that.
"I say that as a dad. I’ve got a 15-year-old boy and a 12-year-old girl. I’m not going to let them grow up in a world where all I’ve got to say to them about their future is, it’s going to be worse than it might otherwise have been.”
It comes after the Labour leader indicated he could be prepared to do a deal with Brussels which would involve the UK taking a quota of asylum seekers who arrive in the bloc in exchange for the ability to return people who cross the English Channel.
Prime minister Rishi Sunak and home secretary Suella Braverman accused Labour of planning to let the UK become a "dumping ground" for 100,000 migrants from the EU each year. But this suggestion has been dismissed by Sir Keir as “complete garbage”.
"The idea that we’re going to join the EU scheme on quotas is complete nonsense. We’re not an EU member and that wasn’t what I was talking about," he told Sunday Morning with Trevor Phillips on Sky News.
Senior Labour figure Pat McFadden, questioned on the same issue on BBC One’s Sunday With Laura Kuenssberg, said: "I don’t think it’s going to be an allocation of numbers, we’re talking about individual cases where a child may have strong family links here.
"It’s not ‘we’ll take this many, you take that many’ - that’s not the kind of negotiation we want to have."