Speaking on Monday, Mr Burnham said he did not think "things have worked out as people said they would at the time, particularly when it comes to immigration."
"I think we've got weaker control now," he said. "The reason the small boats crisis has arisen is because we can't return people, and people know we can't do that in the same way that we used to be able to do."
The prime minister ruled out a return to EU freedom of movement rules without a referendum, after signalling he could include the move in Labour's next election manifesto. He said he was "not proposing any changes in this parliament" and would not move away from the red lines in the Labour manifesto.
Asked whether he would allow the UK to join the EU freedom of movement scheme without a referendum, he said: "No, I mean I wasn't saying that yesterday. I was asked about how things have changed in the 10 years since Brexit, and the truth of the matter is we've lost immigration control in the way that we once had."
On Saturday, the prime minister admitted he was open to reintroducing freedom of movement, a comment that has boosted hopes among campaigners that the UK could look to rejoin the bloc after the next general election. It came weeks after he said the UK could go "all the way" and rejoin, while insisting the British public would "be the boss" of its own future.
Asked whether he would like to see the UK rejoin the EU, Mr Burnham said: "In my lifetime I would like to see that happen but I am not going to move ahead of the public, I am not going to dictate."
More than 200,000 migrants have arrived in the UK after crossing the Channel since data began on 1 January 2018. The record for the largest number of arrivals in a calendar year is 45,774, set in 2022. In the first six months of 2026, the number of people arriving by small boat fell 41 per cent and the number of boats 47 per cent compared with the previous year.