Not every conversation was going so smoothly for Mr. Adonis. At the counter, next to the freshly battered fish, was Darren Fildes, 46, a cafe worker and a Brexit supporter who sees the European Union as “communism with a new pair of knickers,” a British word for underwear.
Yet, with Britain mired in tortuous exit negotiations and its economy slowing, pro-Europeans like Mr. Adonis have begun to sense a change in the prevailing winds and are actively trying to drum up support for another say over the country’s future. Several groups have come together recently and events are being organized across the country to make the case for a new vote.
They argue that, rather than a rerun of the 2016 plebiscite, this new “people’s vote” would decide whether whatever Brexit deal the government finally produces matches up to the extravagant promises made in the raucous referendum campaign.
Mr. Adonis, who sees a looming political crisis over the terms of withdrawal, estimates the prospects of stopping Brexit at 30 to 40 percent.
That may not be as fanciful as it sounds. Any withdrawal deal struck by Britain’s prime minister, Theresa May, will need approval from Parliament, where she has no reliable majority.
Were lawmakers to reject her agreement, Mrs. May would then face three choices, says Dominic Grieve, a pro-European rebel lawmaker in her own Conservative Party. She could try to renegotiate it — unlikely, in view of domestic political pressures and resistance from the European Union — call a general election or put her Brexit plan directly to the people.
A reversal of Brexit, nevertheless, remains a long shot. Neither the government nor Labour, the main opposition party, wants a new referendum, and pro-Europeans face many obstacles, not least drumming up interest among a weary or indifferent populace.
While Britain’s economy is one of the laggards of the Western world, the out-and-out recession predicted by Brexit’s opponents never did materialize. Negotiations on the withdrawal are generally acknowledged to be going poorly for London, steeped in confusion and retreat. But they are so technical that many voters have tuned out and the largely pro-Brexit newspapers pay little heed to British setbacks.
While public opinion has begun to shift against withdrawal, the movement is only slight, according to surveys. Pro-Europeans lack a fresh, credible leader. Former Prime Minister Tony Blair is a prominent, but tarnished, advocate whose reputation in Britain was destroyed by the Iraq war.
But none of that is discouraging a growing cohort convinced they can right what they regard as a terrible mistake. On the first floor of Milbank Tower, near Parliament in London, no fewer than nine pro-European groups have tried to overcome differences, and competing egos, by joining a Grassroots Coordinating Group.
This was nicknamed GCHQ, a lighthearted reference to Britain’s secret intelligence monitoring center, though with posters on the walls, leaflets stacked in boxes and an open carton of breakfast cereal on a table top recently, the room hardly resembles a high-tech spy center.
Among groups based here is Open Britain, which organized more than 300 events on one recent day across the country, and helped start the campaign for “a people’s vote on the final Brexit deal,” fronted not by a politician, but by the “Star Trek” actor Patrick Stewart.
Partly financed by George Soros, the financier and philanthropist, Best for Britain was featured in a controversial article in The Daily Telegraph, co-written by Nick Timothy, a “leave” enthusiast and former aide to Mrs. May. The headline accused organizers of a “secret plot to thwart Brexit.”
In truth, its activities are more humdrum, like the staging of “barnstormer” events, sometimes in leave-voting areas, where pro-European campaigners learn messages and debating techniques.
Though opponents of Brexit are routinely portrayed by critics as members of a discredited, remote elite, Mr. Adonis, a former minister who studied at Oxford University, is unperturbed.
“I am too metropolitan, I am too cosmopolitan,” he said disarmingly, “but I do get out and about.”
His reception seems generally friendly on a tour of 100 areas of the country that voted for Brexit. Face to face, “very, very few people aren’t nice” he said, before adding that “the people who want me hanged or shot say so under a pseudonym on Twitter.”
Cerebral and intense, Mr. Adonis spoke quickly as he analyzed how Britons came to vote against European Union membership, a decision as damaging to their country, he says, as the Suez crisis of the 1950s.
Far from helping those left behind by globalization, he argued, the true agenda of leading Brexit supporters is to shrink the state and extend the laissez-faire policies of Margaret Thatcher. He sees the Brexit vote as a protest from areas with legitimate grievances, and says he thinks that concerns about immigration must be addressed.
There are compelling practical arguments for another referendum, because the 2016 vote was silent on what should replace European Union membership, and those options vary enormously. Since none have a specific democratic mandate, any outcome is likely to be contested for years.
But it is hard to detect a burning public desire for another vote. Outside a shopping mall here in Salford, the main complaint is not about Europe, but about municipal cost-cutting and reduced garbage collection. (“If we can get weekly bin collections, we can stay in the European Union,” jokes Mr. Adonis.)
If it happens, a “people’s vote” will result less from popular demand than from a political impasse. Mrs. May has been embarrassed by defeats on amendments to legislation to quit the bloc in the House of Lords, the unelected second chamber of Parliament, and faces crunch votes to overturn them in the House of Commons soon.
Then, when lawmakers vote on any Brexit deal in the fall, the Labour Party will be crucial. Though its left-wing leader, Jeremy Corbyn, is a lifelong Euroskeptic, most of his lawmakers and party members are not, and analysts say they believe he will oppose any deal that Mrs. May strikes, on the pretext that Labour could do better.
So one strand of the pro-European campaign aims to galvanize Labour Party members — including young people — to pressure Mr. Corbyn to resist Brexit. But another is to start engaging with supporters of Brexit in case there is another campaign.
At an open meeting in Oldham, one of Britain’s most deprived towns, about two dozen people answered a recent invitation from Mr. Adonis to debate Brexit.
Ros Birch, 46, an apprenticeship officer who voted to remain, said it had become clear that the nearly $500 million a week bonanza that Brexit supporters had promised to divert to health spending would never materialize, and pointed to Mrs. May’s problems putting together a deal and getting it through Parliament.
“Whether I am living in cloud cuckoo land or not, I don’t know, but I still don’t feel it will happen,” she said.
But many in Oldham hope it does, including Richard Lowe-Jackson, 58, a self-employed businessman and leave voter, who said he would resent having a second referendum, which he called “a second bite at the cherry.”
During most of the 90-minute discussion, Mr. Adonis stayed quiet and encouraged audience members to speak.
“People like me,” he said, “haven’t been listening enough.”