The Prime Minister said he would not “move ahead of the public” but that he wanted to see the UK return to the bloc within his lifetime and would work to secure a better deal with Brussels.
He insisted a general election would not be called “any time soon” amid speculation he could go to the country early to secure a mandate of his own and put proposals to rejoin to voters following a bounce in Labour’s poll ratings.
Asked about Brexit on ITV’s Good Morning Britain, Mr Burnham said: “I don’t think things have worked out as people said they would at the time, particularly when it comes to to immigration.
“I think we’ve got weaker control now. 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.”
But he added: “I’m not proposing any changes in this Parliament. I’m not going to move away from the red lines that were in the Labour manifesto.
“I am respecting what I said to the voters in Makerfield, but I’m not going to say this morning, sitting here, that the deal we’ve got at the moment is good enough for Britain. I don’t think it is good enough for Britain.
“I think we can make it better and I’m going to lead a discussion about how do we make it better in a way that people can support.”