LONDON — The Labour Party canvassers gathered after dark outside a tube station in Pimlico, a pocket of central London that, by all appearances, should be fertile terrain. Nearly three-quarters of the surrounding district voted to stay in the European Union, among the strongest “Remain” votes in Britain, putting the pro-Brexit Conservatives at risk in a seat they had held since the district lines were drawn in 1950.

But the district, the Cities of London and Westminster, with its rows of white stucco townhouses and crowded housing projects, may now become a parable on the left for why Prime Minister Boris Johnson holds a commanding position less than two weeks before the election.

Brexit has sent tremors through the British political system, shaking up the traditional left-right, class-based divisions. While the Conservatives have capitalized on the upheaval, building a coalition of pro-Brexit voters across regional and class lines, the left has so far struggled to win converts and overcome its own divisions.

With Mr. Johnson still deeply unpopular, undecided voters may yet swing Labour’s way. Recent polls suggest the Conservative lead has begun to shrink, putting many seats with razor-thin margins potentially in play. But Labour’s leftist leader, Jeremy Corbyn, has lately dug in against accusations of anti-Semitism in the party and criticisms that his Brexit policy was incoherent.

Setting off from the tube station last week, the scores of Labour canvassers were quickly confronted with a treacherous political rip tide: Labourites turned off by Mr. Corbyn; die-hard Remainers who, fed up with Labour’s ever-evolving stance on Brexit, had decamped to the staunchly anti-Brexit Liberal Democrats; and even former Remainers who now resignedly conceded that democracy demanded Brexit be done.

“It’s desperate times — it’s very difficult to know how to vote,” Philip Rudge, 73, who lives in the east of the district, said a few days earlier. “I’ve been Labour all my life, but I’ve been dismayed to see the infighting and back-stabbing and so on. Corbyn’s not a leader. Labour will have to win an election against the leadership.”

This London district, known informally as the Two Cities, is in many respects a mirror image of pro-Brexit, working-class Labour strongholds in northern England being targeted by the Conservatives. Stocked with bankers and lawyers who once made up the Conservative base, but who want to stay in the European Union, the Two Cities is precisely the kind of seat that Brexit could help deliver to a left-leaning party.

In the Two Cities, the left is also suffering from a second problem: the anti-Brexit vote being split between Labour and the Liberal Democrats, a smaller, more centrist party that has stormed back from obscurity by arguing for lawmakers to summarily reverse Brexit.

Anti-Brexit activists are pleading with people to vote tactically — meaning to vote for whichever Remain party stands the best chance of winning a given seat — and polls suggest that Britons are doing so in greater numbers than before, for good reason. While there are roughly half a dozen parties in Britain’s Brexit-battered Parliament, only one can win any given seat: When supporters of a given cause split their votes between several candidates, they risk letting an opponent come through the middle.

But disagreements on the economy and foreign policy still run deep on the left. And with the Liberal Democrats neck-and-neck with Labour in districts like the Two Cities, that has left even the most calculating anti-Brexit voters confused about what to do.

“I would say I’m a tactical voter normally, but it’s not clear at this stage what the tactic should be,” said Fern Watson, 36, who is opposed to Brexit, bracing against the cold in the Barbican, a brutalist estate on the eastern edge of the district. “I don’t really see either Labour or the Lib Dems as my natural political home, and I think a lot of people of my age and education level feel the same.”

She had visited three different websites purporting to tell people how to vote in individual precincts to stop Brexit. One of them said Labour, and the other two the Liberal Democrats.

Current polling suggests the Remain vote will split in the Two Cities, allowing a weakened Conservative candidate to hold the seat. Across the country, were only 120,000 more Remainers to vote tactically, one analysis showed, that would be enough to defeat Mr. Johnson on Dec. 12.

But for now, in crucial London districts, the race has become a battle of bar charts, as both Labour and the Liberal Democrats try to prove they are best positioned to win three-way fights for seats. Labour has printed reams of them showing how it cut into the Conservatives’ lead in the 2017 election, capitalizing on the same shifts that have turned American cities into progressive bulwarks.

But the Liberal Democrats, relying on more recent polling, have distributed their own sheafs of charts with exactly the opposite message.

Couple that with the hazy mechanics of how a left-wing coalition would actually try to stop Brexit, and Remain voters are stuck in a confusing predicament.

“If you are a Leave voter, the route to your destination is now really clear and simple,” said Rob Ford, a politics professor and the editor of “Sex, Lies and Politics: The Secret Influences That Drive our Political Choices.” “Whereas if you’re on the Remain side, what’s the route to your desired destination? It’s as clear as the channel on a foggy day right now.”

Remain voters are torn by Mr. Corbyn’s cautious, some would say muddled, Brexit policy, in which he would negotiate a new exit deal with Brussels and then put it beside Remain in a public vote in which he himself would stay neutral.

One voter, Philip Jeremy, 60, asked about Labour’s Brexit policy, said bluntly: “Corbyn doesn’t have one.” So desperate is Mr. Jeremy not to see either major party steering the country that he said he wanted the election to deliver no clear signals at all.

“I prefer a hung Parliament, just so none of them do anything too drastic,” Mr. Jeremy said.

Sitting as it does at the heart of London, the Two Cities district covers not only Buckingham Palace and Parliament but also the well-mannered homes of many senior lawmakers, making it a trophy scalp for the opposition.

But it also has considerable areas of poverty, where allegiances to Labour are strong and its message should resonate: The party has focused heavily on health care, housing, climate change and income inequality.

Those policies have drawn some pro-Brexit voters into the fold, like Jalil Abdul, 75, who has lived for four decades in Walden House, a public housing block in Pimlico that had been targeted for redevelopment by a 28-year-old billionaire.

“This year, I like the Labour Party,” Mr. Abdul said, “because for the last three years the Conservative Party has failed at doing anything.”

But polls suggest many anti-Brexit Conservatives are sticking by Mr. Johnson, not out of love and admiration for him as much as fear and loathing for his opponent, Mr. Corbyn.

“We have a choice of one of two prime ministers, either Boris, or Jeremy Corbyn,” said Christopher Wyke, 64, a Conservative who lives and works in the City of London, the financial district, and who himself supports Brexit. “If you vote for anybody but the Conservatives, you risk getting Corbyn, so there’s no choice. Even people who are Remainers, they still don’t want Corbyn. He’d be infinitely more dangerous.”

And the Liberal Democrats have alienated some voters who might otherwise be amenable to their centrist economic policies by taking a stark position on Brexit: revoking it altogether, without a public vote.

Even anti-Brexit Labourites are no longer a shoo-in to vote against the Conservatives.

Gordon Nardell, the Labour candidate, broke off from the party activists outside the tube station last week to knock on some doors alone. The first answer seemed to startle him: a middle-aged man who said he was a longtime Labour supporter and backed Remain in 2016, but now wanted Mr. Johnson to get Brexit done.

“The vote was to leave, so you know, recognize the vote,” the man said. “To me, once you vote, that’s it — you either accept it, or if you don’t accept it, democracy means nothing.”