A U.K.-EU summit is scheduled for next month, although that is set to focus tightly on technical tweaks to the existing relationship rather than addressing bigger questions of Britain's future ties to the bloc.

Burnham's decision to reignite debate in Britain about the EU has already provoked a bullish response from some of Brexit's leading cheerleaders.

Speaking at a Westminster press conference Monday, Nigel Farage said rejoining the bloc would be “utterly moronic” and argued Brexiteers would win a referendum on reversing the result “very comfortably.”

“Listen, Brexit would not have happened if I had not been born — all right, simple as that," the Reform UK leader said Monday. "Yes, there were some Johnny-Come-Latelies. They came in at five minutes to midnight. Am I up for the fight again? You bet your blooming life I am.”

Sam Blewett contributed to this report.