A UK Cabinet minister has played down any suggestions of a split between Rishi Sunak and James Cleverly over the controversial Rwanda asylum plan, after the Home Secretary said it was not the “be all and end all”.

The remarks, which came amid a separate row within the Tory party about record levels of net migration to the UK, raised eyebrows among some in the party.

But Chief Secretary to the Treasury Laura Trott, a recently promoted ally of Mr Sunak, insisted the pair were on the same page.

Mr Cleverly said, in an interview with The Times, that the initiative is not the “be all and end all” to stopping Channel crossings.

He added: “My frustration is that we have allowed the narrative to be created that this was the be all and end all.”

Mr Sunak, in contrast, used an interview with The Mail On Sunday to stress the importance of the scheme, after the Supreme Court ruled it unlawful earlier this month.

Read more: Tory civil war erupts as UK net migration reaches record high

Speaking to the Sunday Morning With Trevor Phillips programme on Sky News, Ms Trott said: “They’re both actually saying the same thing, which is that Rwanda is part of our plan.

“Both saying it is part of the plan, it is not all of the plan.”

Mr Sunak has pledged not to let a “foreign court” stop flights to Rwanda, with plans for a new treaty and emergency legislation to ensure the plan is legally watertight.

It was the UK Supreme Court, rather than “a foreign court”, that dealt the latest blow to the UK Government’s hopes of sending asylum seekers who arrive in the UK on a one-way trip to Rwanda.

But Tories are keen to ensure that the ECHR and the Strasbourg court that rules on it will not prevent the policy, first announced in 2020, from being implemented.

Ms Trott said: “We have successfully in the last year bought the numbers of people coming over here illegally down by a third.

“That is at a time when the numbers coming into Europe are up by 80%.

“This was not a foregone conclusion.”

Read more: Poll: Two-fifths of Scots want to see an increase in immigration

The Cabinet minister declined to spell out any new steps the UK Government might take to reduce overall net migration, another preoccupation of Tory MPs.

The figure peaked at 745,000 in the year to December 2022, according to revised estimates published by the Office for National Statistics (ONS) on Thursday.

The data places migration levels at three times higher than before Brexit.

Immigration minister Robert Jenrick is understood to have worked up a plan designed to appease calls from right-wing Tories for the Government to take action.

He is pushing for a ban on foreign social care workers from bringing in any dependants and a cap on the total number of NHS and social care visas.

His plan would also scrap the shortage occupation list, a programme that allows foreign workers to be paid 20% below the going rate in roles that suffer from a lack of skilled staff.

But Ms Trott, who said immigration levels are “too high”, declined to shed any light on what potential measures could be introduced.

Labour has sought to win over voters dissatisfied with the Tory record.

Shadow home secretary Yvette Cooper told the Sunday Times her party would increase salary requirements for workers coming from overseas.

The Labour MP said that her party would change current rules that allow employers to pay migrant workers 20% less than the annual salary threshold of £26,200 for roles on the shortage occupation list.

Read more: Blow for Sunak as Supreme Court rules Rwanda policy 'unlawful'

Appearing on the BBC’s Sunday With Laura Kuenssberg, shadow chief secretary to the Treasury Darren Jones signalled that Labour sees a “normal level” of migration at a “couple of hundred thousand a year”.

“But it depends on the needs in the economy,” he added.

Asked if Labour could bring numbers down within the first term of a government, he said: “I think we probably would hope to do that, yes, but we’ve talked about a decade of national renewal.

“Not because we’re being presumptuous about this election, or indeed the next one, but because we think the deep structural problems that we’ve been left from the Conservatives after the last 13 years, it’s going to take time to fix and it’s going to take time to turn around.”