• There's been one main narrative since the U.K.'s Conservative Prime Minister Rishi Sunak called a general election back in May — that the opposing Labour Party would win the vote by a landslide.
• UK voter polls have more or less pointed in one direction, giving the center-left Labour Party around a 20-point lead on the Conservatives.
• The party has been reluctant to reference the polls, telling CNBC it did not comment on projections, as they "vary and fluctuate."

LONDON — There's been one main narrative since the U.K.'s Conservative Prime Minister Rishi Sunak called a general election back in May — that the opposing Labour Party would win the vote with a landslide.

While voter polls may have differed in scale and methodology, the results have pointed in one direction, showing that the center-left Labour Party has around a 20-point lead on its main rival, the Conservatives. Labour is on track to win around 40% of the vote while roughly 20% of the support is projected to go to the Tories, according to a Sky News poll tracker.

Labour candidates and leader Keir Starmer have been keen to play down the level of support that the party enjoys, fearing voter complacency and the appearance of "having it in the bag" — a stance that could prompt voter apathy and a lower turnout of supporters at the polls, or a backlash from Conservative-inclined sections of the electorate.

"The Labour Party wants to be able to be convince voters that it's absolutely central that they turn out and vote, because otherwise the Tories will win, and the Tories are desperate for people to think that they have still got a chance, and therefore it's worth turning up," Britain's top polling expert John Curtice told CNBC.

Question marks have risen in the past over the accuracy of British voter polls, with previous projections over or underestimating support for various political parties. The errors have often come about because of inadequate sampling or of factors that are harder to control, such as voters being "shy" when polled on which party they intended to support.

This year, however, experts tend to agree that the polls show such a swing to Labour that, even if the scale of support were wrong, the overall result would be the same: a convincing win for the opposition party.

"My attitude is [that] a poll should be taken but not inhaled," Curtice, a professor of politics at the University of Strathclyde, and senior research fellow at the National Centre for Social Research, said wryly.

"The point is, you shouldn't be looking at them to provide you with pinpoint accuracy, they should give you a reasonable indication of the direction of travel."

"It just so happens that because this is an election in which apparently one party is so far ahead, much as [it was] in 1997, the polls could be quite a bit out — but nobody will notice," he noted, referencing the year when the Labour Party won a landslide against the Conservatives, ending the latter party's then 18-year rule.

Labour 'spin'?

The Labour Party itself is understandably keen to downplay the polls, with a spokesperson telling CNBC that the party doesn't comment on projections, "as they vary and fluctuate."

"Instead, we're working hard to take our message of change to voters ahead of the only poll that matters, on 4 July," the spokesperson stated.

On Monday, Keir Starmer said no vote should be taken for granted, asking his supporters to continue campaigning until polls closed on Thursday.

"The fight for change is for you, but change will only happen if you vote for it. That is the message we have to take to every doorstep these last few hours and days until 10 o'clock on Thursday night."

"Nothing must be taken for granted, every vote has to be earned. The polls don't predict the future, we have to get out there," he told campaign supporters in Hitchin.

Labour's former campaign and communications directors, Alastair Campbell, one of the chief strategists behind the rebranding of the party in the 1990s as 'New Labour' ahead of its monumental election win in 1997, told CNBC that he doubts current voter polls.

"I get really worried about about the way that these election debates are now unfolding, virtually everything in the debate at the moment is about these opinion polls," he told CNBC two weeks ago.

"Apart from a few postal votes, nobody's voted yet. And I just do not for one second believe that the Conservatives are going to get virtually wiped out, I just don't believe it," he said.

"I just think there's something going very, very wrong with these polls, I could be completely wrong, and it's true that Labour have been consistently ahead. But I just wish that, in our election periods, we would talk less about polls and more about what the parties are saying."

Polling expert Matt Beech, director of the Centre for British Politics at the University of Hull, said Campbell's position was designed to persuade Labour-inclined voters to cast their ballots.

"They want to make sure that they get as big a majority as possible. They're all very much aware of [the lead-up to the election in] 1992 with the phenomenon of 'shy Tories,' when the polls said Labour would win and they didn't .... [But] they're not actually that genuinely worried about that. What they want to have a 1997-like landslide tsunami," Beech told CNBC.

He added, "So if you keep banging on that drum [that the polls are not correct], you're going to say to Labour-inclined voters, 'please go out and vote.' But it's not that 'we're actually scared we're not going to win, we are going to win comfortably. But we want a majority that enables us to push our agenda and we want this win to mean that we're there for two terms'," he noted.