The Conservative leadership contest must be drawn to an early end so the victor can respond to Labour’s first Budget, Robert Jenrick has said after making it through to the final stage of voting.

The leadership hopeful issued a challenge to Conservative Party headquarters – which is responsible for running the contest – to bring it to an end before October 30, as he made his first public appearance since he made it through to the final two in the race to succeed Rishi Sunak.

In a speech at the Policy Exchange think thank, Mr Jenrick said he would be the candidate to “heal” the Tories after years of infighting.

But he also signalled his rival, Kemi Badenoch, had not provided a clear vision of what her leadership would look like.

Mr Jenrick denied suggestions there had been vote trading among the different campaigns, after James Cleverly suffered a shock exit in the final round of voting among Tory MPs on Wednesday.

Mr Jenrick and Ms Badenoch have until November 2 to make their case to members, when the final result will be announced.

In his first speech of the final heat, he told an audience in central London the Conservatives had been “characterised by disunity, by petty squabbling, and by differences that need to end”.

He added: “I want to heal the party, I want to settle the big policy debates that we have had now, so that we can unite around a clear policy platform and we can take the fight to Labour and provide the effective opposition that the country is crying out for.

“That should begin immediately, in fact, it should begin with the Budget.

“I want to be the leader of the opposition who is stood up in the House of Commons giving the response to Rachel Reeves at the end of the month.”

The Tory former minister had earlier said he wanted to use the leadership race to “settle some of the big questions facing our party and our country”.

Conservative leadership bid
Conservative Party leadership candidate Robert Jenrick delivers a speech at Policy Exchange in London (Jordan Pettitt/PA)

In what appeared to be a swipe at his rival, the Newark MP added: “That was surely the purpose of having this long contest. Not to spend months debating personalities, not to say there will be a plan tomorrow but we don’t know what it is.

“That is a recipe for more infighting and for more loss of public trust. So what I stand for, and this does differ from some of the other candidates that have put themselves forward over the course of this contest, is I have set out very clear policy answers.”

Mr Jenrick, a former immigration minister, also warned the Conservatives would not survive if they do not “get serious” about migration.

“I say leave the ECHR, cap migration in the tens of thousands and regain the trust of the British public,” he added.

On Mr Cleverly’s shock elimination from the race, Mr Jenrick conceded there was “always horse trading in these things”.

But he added: “We did not trade any votes. We worked relentlessly to persuade colleagues to get the greatest number of supporters we could in Parliament.”

Elsewhere a group of centrist Tories has refused to endorse either of the final two candidates.

The Tory Reform Group (TRG), which describes itself as “the home of One Nation Conservatism since 1975” said in a statement that both candidates have “used rhetoric and focused on issues which are far and away from the party at its best, let alone the One Nation values we cherish and uphold”.

Some of the TRG’s patrons include serving MPs who have, however, individually declared their support for one of the remaining candidates.

For example, shadow Treasury minister Nigel Huddleston is supporting Kemi Badenoch, while shadow Scotland secretary John Lamont has signalled his support for Robert Jenrick.