Chancellor tells group of backbench Tory MPs that if his changes are not passed £15bn worth of cuts will have to be found

George Osborne has fended off Conservative MPs anxious at proposed cuts to tax credits at a private meeting of party’s 1922 backbench committee, by insisting the changes have to go ahead and warning that if he had not acted then £15bn worth of spending cuts would have to be found elsewhere.

In a Treasury analysis released to coincide with the backbenchers’ meeting, the government said if it had not acted, spending on tax credits would have risen to £40bn by 2016-17, a £10bn rise from 2010-11 and £15bn higher than now forecast as a result of the cuts being introduced by Osborne in the summer budget.

Osborne faced close questioning from both wings of the party about the measures that some MPs fear will be seen to be hitting the “working strivers” that the Tories promised to help at the election.

The chancellor told backbenchers he was not prepared to relent on an issue that he regarded as the most serious vote at this stage of the parliament. Some backbenchers left the meeting with the impression that Osborne must have realised he will have to make changes.

The Treasury also issued an analysis to show that if the £15bn worth of welfare cuts were not made, and no other tax changes are made, the government would have to lose the equivalent of around 200,000 nurses and 70,000 doctors; or around 325,000 teachers, or more than the entire Home Office budget.

In a further effort to drive home to Tory MPs the necessity of the cuts to tax credits, he said the £15bn was the equivalent of more than has been spent since on increasing the personal allowance to date, or £500 a year extra in income tax for every taxpayer.

He also pointed out that if the 2010 tax credits system was still in place, support would still be available to families earning well over £50,000 a year.

In a further attempt to rally nervous troops before a Commons debate on the issue on Tuesday, Treasury chief secretary Greg Hands said: “Labour has opposed every single saving we’ve made in a welfare budget they let spiral completely out of control.

“When they left office, they had allowed means-tested payments to go so far up the income scale that nine out of 10 families – including MPs – were eligible.

“Treasury analysis now shows that without the reforms we have embarked on, spending on tax credits would be rising to £40bn next year. Instead it’s forecast to be £25bn.

“That £15bn that we’ve saved – while at the same time offering working people lower taxes and higher wages, thanks to our new personal allowance of £11,000 from April and the new ‘national living wage’ – is the equivalent to £500 extra in income tax for every taxpayer.

“Labour must now explain where the money is coming from.”

Earlier Boris Johnson, London mayor and Conservative MP for Uxbridge and South Ruislip, said he believed the tax credit changes were under “intensive review”.

“Let’s see what they come up with,” he told BBC Radio 4’s World at One. “I’m sure that they are working on it now.

“Believe me, we’ve all been talking about it. This is something that is under intensive review and consultation at the moment. I have no doubt that people are working very, very hard right now to try to make sure that as we reform the tax credit system, we do so in such a way as not to bear down too unfairly on hard-working people on low incomes in London and elsewhere.

“I’m sure that, irrespective of the politics of it, nobody wants to do something that is not fair to working people.”

Johnson stressed that Osborne was “completely right” to try to reform the tax credit system.

He said: “Be in no doubt that the tax credit system as it currently stands cannot go on. The chancellor is completely right to want to reform it. I think it’s brave, it’s right.

• This article was amended on 20 October 2015 to clarify that the government said that if it had not acted, spending on tax credits would be £15bn higher, not lower, than now forecast.