New Delhi, Oct. 28 -- Prime Minister Andy Burnham, who marked his 100th day in office on Tuesday, has broken that code of silence and reignited a debate that bitterly divided the country. He says Brexit has been a failure and the U.K. should seek a much closer relationship with the EU, with options up to and including rejoining the 27-nation bloc.

"I am positive about closer ties with Europe and I'm not hiding that," Burnham told the Sunday Times. "I think it will add to British GDP. I think it will give us stronger control of migration. I want to make those arguments."

In recent interviews, Burnham has said the country should have an "evidence-based debate" about the consequences of Brexit. He gave the example of immigration. Supporter...