The Tory leadership contest should be “wrapped up quickly” and future leadership election processes could be reviewed to hasten them, a minister has suggested.

James Cleverly said it would be “legitimate” to review how future Tory leadership contests are carried out.

The race to become the next prime minister began on July 12 and results are expected on September 5.

As Liz Truss and Rishi Sunak continue to make their pitch to Conservative members, research by the University of York has warned that two thirds of UK households will face a financially precarious situation this winter owing to rising energy bills.

The NHS is meanwhile facing long backlogs for care, and rail workers continue to strike.

Asked by LBC Radio if it was appropriate to hold weeks of leadership election hustings while these events continue, Education Secretary James Cleverly said: “This is the system that is in place. I do think it is legitimate to look at reviewing that.

“That is an internal party process rather than a Government process, but as I say, Government does continue, ministers are still working.”

Pressed about whether it was a “bad look” to continue with the contest while the energy crisis unfolds, he added: “I would have been happy if this whole process was over more quickly, but as I say one of the people contending for this is a backbencher not involved in government at all any more, Liz is the Foreign Secretary and I know that she is still active in the foreign affairs side of things as well.

“But yes, of course we would like to see this wrapped up quickly, but we are still working nonetheless.”

The leadership contest has seen growing hostilities within the ranks of the Conservative party, which is traditionally characterised by its unity and discipline.

Mr Sunak has lambasted Ms Truss’s plans to cut taxes as unrealistic, and said it would be a “moral failure” for her to not do more to address rising energy costs.

A spokesperson for his campaign also claimed that analysis by the Institute for Fiscal Studies, which claims long-term tax cuts were “unsustainable”, had driven “a coach and horses” through the Foreign Secretary’s economic plan.

Jacob Rees-Mogg, a prominent support of Ms Truss, has attacked former chancellor Mr Sunak for not giving his full backing to a Whitehall cost-saving push.

Mr Rees-Mogg said: “Earlier this year, the Efficiency and Value for Money Cabinet Committee was established with a mission to save the taxpayer over £5.5 billion each year.

“This was sadly under-utilised by the former chancellor, but it must be a vital tool in the next prime minister’s arsenal for cutting waste and inflation.”