Kemi Badenoch has called for foreign nationals to be barred from claiming disability and sickness benefits, as she set out plans for tighter curbs on welfare.

In a speech on Thursday, the Tory leader described Britain’s benefits bill as a “ticking time bomb” that could “collapse” the economy.

It comes after the party outlined some of its own proposals to reduce spending, after Labour largely gutted its own plan for benefits cuts after a backbench revolt.

Legislation to bring in remaining government cuts to sickness benefits was approved by MPs on Wednesday evening.

But other proposals, including changes to the eligibility criteria for disability benefits, have effectively been put on hold.

The government announced plans to shrink welfare spending in March, warning the working-age welfare bill was set to rise by nearly £30bn by 2030 and reforms to the system were required to ensure it remained sustainable.

It wanted to make it harder to claim personal independence payment (Pip), the main disability benefit in England, Wales and Northern Ireland, and make health-related top-ups for universal credit less generous.

But ministers significantly watered down the cuts earlier this month after a huge rebellion from Labour MPs, all but wiping out savings estimated to be worth £5bn a year by the end of the decade.

Plans to freeze the higher rate of universal credit for existing health-related claimants have been reversed, whilst all changes to the Pip system have been parked pending a government review into the assessment regime.

In her speech on Thursday, Badenoch accused Labour of being “beholden to left-wing MPs” and “turning a blind eye” to rising benefit costs.

She also sought to create a dividing line with Reform UK over the two-child benefit cap, which Nigel Farage’s party has pledged to scrap, branding him “Jeremy Corbyn with a pint and a cigarette”.

“On welfare he shows his true colours – promising unaffordable giveaways with no plan to fix the system,” she said.

Labour is under pressure from some of its own MPs to lift the cap, which was introduced under the Conservatives and prevents most families from claiming means-tested benefits for any third or additional children born after April 2017.

A Labour spokesperson said: “The Conservatives had 14 years to reform welfare – instead, they left the country with a broken system that holds people back and fails to support the most vulnerable.”

The party also warned that the Conservative proposal could see disabled British nationals living abroad being denied support if other countries decided to take a similar approach.

The Conservatives have not backed the government’s legislation to deliver changes to the welfare system, arguing its proposals do not go far enough.

They have proposed that disability and sickness benefits should only be paid to British citizens, with exceptions for those covered by international agreements, such as citizens from EU countries who have acquired settled status in the UK.

At the moment, foreign nationals gain access to the welfare system when they are granted indefinite leave to remain or refugee status. Applicants for Pip generally need to have lived in Britain for at least two of the last three years.

Asylum seekers are not allowed to apply for benefits, although they have access to taxpayer-funded accommodation and separate financial support.

“We can’t afford to be spending a billion pounds a month on benefits for foreign nationals,” Badenoch said.

“It is not unreasonable to expect someone to have paid in and become a British citizen before they unlock access to sickness benefits.”

The party says figures obtained under freedom of information laws show universal credit payments to households containing at least one foreign national stood at £941m a month as of March.

But working out the exact scale of payments to non-UK nationals specifically is complicated, because the Department for Work and Pensions does not provide a breakdown of claimants by immigration status and nationality.

However, the department is due to publish the first such breakdown next week, and has committed to updates every three months thereafter.

Other Tory proposals include limiting access to Pips and the health-related part of universal credit to those with “less severe” mental health conditions, and preventing claimants from receiving payments without a face-to-face assessment.