A poll suggests that Tory voters are worried that Angela Rayner would eventually replace Sir Keir Starmer in Downing Street.

Supporters of Ms. Rayner as Sir Keir's successor were twice as likely to be Labour voters as Tory ones.

Only 13% of 2019 Conservative voters agreed with the 28% of Labour voters who supported the deputy leader's candidacy.

The nomination of the shadow chancellor, Rachel Reeves, was far less contentious; she received support from 13% of Conservatives and 18% of Labour members, surpassing both the shadow aid secretary Lisa Nandy and health spokesman Wes Streeting.

Ms Rayner was the most popular choice among Labour voters, which will lead to fears that Sir Keir could be followed in office by his much more Left-wing deputy.

With separate surveys suggesting as few as 35 per cent of 2019 Tory voters will stick with the party on Thursday July 4, the findings raise the prospect that those who have turned to Labour believe that Ms Rayner could eventually replace Sir Keir.

Ms Rayner is one of a few senior Labour figures who has been happy to term herself a “socialist”.

She has pledged a radical workers’ rights agenda under which all Tory legislation affecting trades unions brought in since 2010 would be repealed.

Ms Reeves refused to serve under Jeremy Corbyn and has built up close relations with business, scrapping previous policies such as a cap on bankers’ bonuses.

The Savanta poll for the Daily Telegraph also showed that Labour’s lead over the Conservatives has narrowed to its lowest for a month as the election campaign reaches its end.

The Tories were on 24 per cent, up three – the highest figure since before Rishi Sunak’s D-Day debacle in early June.

Labour has also increased by one point to 39 per cent. Sir Keir Starmer’s lead of 15 points over Mr Sunak is still likely to result in a Labour landslide but it could save the Conservatives from electoral oblivion.

Meanwhile Reform UK saw another decline by one point to 13 per cent, the Liberal Democrats fell by the same amount to 10 per cent and the Greens suffered a two-point loss, leaving them on four per cent.

Almost half of the public said their impression of Mr Sunak had worsened during the campaign, including 31 per cent of those who voted Conservative in 2019.

His decision to leave June’s D-Day ceremony early is seen as the biggest gaffe of the campaign, the poll suggested.

Chris Hopkins, political research director at Savanta, said: “This is the highest Conservative vote share in a Savanta poll since early June - or more specifically, pre D-Day debacle.

“Let’s not get ahead of ourselves here: this result, if replicated on election night, would still mean a historic Labour victory.

“But these sorts of numbers imply heavy losses rather than electoral oblivion. Alongside Reform UK looking like they could be slipping, this is as close to good news as the Conservative Party gets these days.”

The poll of 2,287 adults, was carried out between Wednesday and Friday last week. On Wednesday night, Mr Sunak was seen to have bested Sir Keir on immigration in the final leadership debate of the campaign.

However, the survey showed that only Labour is perceived to have run a positive campaign, with 45 per cent saying so compared with 32 per cent who said it was negative.

Reform UK’s campaign was seen by 45 per cent of people to have been negative, with 27 per cent rating it positive. The Conservatives were considered to have run a positive campaign by only 22 per cent of people compared with 56 who thought it had been negative.

The general perception of Sir Keir has remained net neutral over the course of the campaign, as it has for Sir Ed Davey, the Lib Dem leader.

For the other two leaders, the public are far more likely to say that their opinion has worsened rather than improved.

A quarter said their opinion of Reform’s Nigel Farage had improved but four in ten said it has worsened. For the Prime Minister, half said their opinion had worsened with just one in six saying it had improved.

Mr Hopkins said: “This campaign is not the only reason the Conservatives are in a deep trouble, but it certainly hasn’t helped.

“The public thinks that the Conservatives have run the most negative campaign out of all the major parties, and half say their view of Sunak has got worse since the election was called. I’d imagine that’s the opposite of what the Conservative Party were hoping.”

Some 20 per cent of voters said that Mr Sunak’s D-Day departure was the most damaging campaign gaffe or misstep, closely followed by Reform UK candidates caught on film making racist slurs (17 per cent) and the betting scandal (16 per cent).

Mr Sunak saying he went without Sky TV as a child was listed by 11 per cent of voters, the Labour candidate betting against himself 6 per cent and Labour’s mishandling of Diane Abbott’s candidacy 5 per cent.

The biggest mishap for 4 per cent was Mr Sunak announcing the date of the election in the pouring rain, followed by Jeremy Corbyn, the former Labour leader, running as an independent (2 per cent) and Mr Farage having milkshake thrown at him (1 per cent).