The French finance minister has invited the UK to “come all the way back” to the European Union after Andy Burnham raised the prospect of a new referendum to reverse Brexit.

Roland Lescure was speaking after the prime minister used his Labour conference speech to pledge that the government would explore closer ties with the bloc at a summit later this year.

He used subsequent interviews to spell out how wide-ranging his consideration of Britain’s future with Brussels could be because Brexit had caused “more harm than good”.

Asked about Burnham’s comments, Lescure told the BBC: “British people decided, and that’s obviously their 100% right, and if they’re willing to come back, they will have to decide. But what I can tell them is: come back, anytime.”

Lescure said he wanted Britain back in the union to face emerging global threats together.

Burnham said last week that the government’s options included keeping the current arrangements in relation to the UK’s relationship with the EU, seeking a customs union, returning to the single market, or going “all the way” with full membership.

He said ministers would examine “what is doable” and the “pros and cons” of each option.

The prime minister is travelling to Germany for talks with the chancellor, Friedrich Merz, whose government has been supportive of Burnham’s suggestion that the UK could explore closer links with the EU.

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Burnham and Merz are expected to agree on a deal for closer security cooperation against cyber-attacks on European countries but the two will also discuss UK-EU relations.

Lescure also responded to comments by Burnham that EU rules to help European manufacturers would damage the UK.

British government sources warned days earlier that the “EU reset” summit would be delayed again unless the bloc agreed to discuss legislation that could lock British business out of parts of EU industry.

“Come back, and you’ll be at the table, and we discuss all these things together,” Lescure said.

Nigel Farage has claimed Burnham has given him “the biggest boost in my career” by reviving the Brexit debate, which the Reform UK leader said had reopened a “huge flank” to his party.

Dismissing polls showing that as much as 59% of the public favoured rejoining the EU, Farage said: “Of course they do, until you tell them it’ll cost 25bn quid a year, until you tell him it’ll mean joining Schengen [the area of Europe that has open borders], until he tells them it will mean actually having to recommit to joining the euro.”