Sir Keir promised he would allow EU nationals to move freely to the UK during his leadership campaign. But he said yesterday he has no plans to push for a "major renegotiation" of the Brexit trade deal secured by Boris Johnson.
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He said: "Whether we like it or not that is going to be the treaty that an incoming Labour government inherits and has to make work.
"It is not being straight with the British public to say you come into office in 2024 and operate some other treaty. We have to make that treaty work."
He added: "I don't think there is a case for rejoining the EU, I've said that before. But I think pretending to the British public that somehow after four years' negotiation the treaty that has just been secured is going to be up for the grabs and that the EU are going to start saying 'Let's start all over again', that is not realistic."
Sir Keir was behind Labour's Brexit policy under Jeremy Corbyn and was a prominent Remainer.
The Labour leader ordered his MPs to back the Prime Minister's trade deal in the Commons last month as he tried to draw a line under the Brexit divisions in his party that led to one of its worst general election defeats.
But last week Labour MP Rosie Duffield admitted most of the party is "desperate to rejoin" the EU.
Sir Keir said that Labour voted for the free trade agreement because the alternative was no deal but it needed improving.
"If you look at the creative industries and how they are going to operate across borders, there are huge gaps for them. The service sector has largely been left out.
"But I don't think that there's scope for major renegotiation. We've just had four years of negotiation. We've arrived at a treaty and now we've got to make it work."
He said it was not as promised "but better than no deal" and it now needs to work.