The head of parliament's independent watchdog has claimed there is significant public support for giving MPs an 11% pay rise worth almost £8,000 after the next election as part of a package of reforms, despite David Cameron's demand that he drop the proposals.

Sir Ian Kennedy, chairman of the Independent Parliamentary Standards Authority (Ipsa), called for an end to the "yah-boo politics" about MPs' pay as he insisted the increase to £74,000 would go ahead as planned, along with cuts to expenses, perks and pensions.

Ipsa's refusal to back down on Thursday created a stalemate, as the three political party leaders found themselves helpless to intervene unless the government legislates to scrap the body set up to determine MPs' pay in the wake of the 2009 expenses scandal.

Ed Miliband, the Labour leader, has demanded a meeting with Kennedy to tell him the proposal "does not command public confidence" but neither Cameron nor Nick Clegg, the Liberal Democrat leader, are planning to take part in any cross-party talks to settle the matter.

Unless Ipsa changes its mind, the package of reforms will remain up in the air until a review in 2015, potentially making pay for MPs a toxic election issue.

On Thursday, Kennedy appeared unlikely to modify his opinion, arguing the proposals would not cost the public "a penny more" and warning that overturning his judgment could create another expenses scandal.

"This is a package, a package of reforms," he told the BBC's World at One programme. "You cannot unpick it. You can't say that bit we like and that bit we do not ... The package as a whole has significant support from the public. The public is far more sophisticated than a lot of people think they are."

Under the changes, MPs would be paid £74,000 – an increase of 11% on the current level, or 9.26% on the likely level in the year before the change.

Ipsa also recommended that pay be linked to average earnings, and pensions be put on a par with those in other public sector jobs. It would scrap "resettlement payments" worth tens of thousands of pounds when MPs leave the house and replace them with more modest loss-of-office payments, which will be available only to those who contest their seat and lose. There will also be a new regime of business costs and expenses, including ending the provision of free evening meals on some days when the House of Commons is sitting late.

Responding to the announcement, Cameron insisted the proposals were not a "final recommendation" and repeated his threat to take action if there was no change in the plans during the review in 2015.

"They should think again and I very much hope they do. I don't rule out, and I don't think anyone rules out, taking action if they don't modify this proposal," he said.

A one-off pay increase at a time of public sector wage restraint was "not on", he added. On Thursday morning, Clegg also described the prospect of a rise as "incomprehensible".

However, Miliband said this reaction did not go far enough to resolve the uncertainty and wrote to Cameron demanding an immediate meeting with him, Clegg and Kennedy.

"The independent body charged with this are just wrong. I have to account to the British people, they don't have to account to the British people, and I know that this proposal does not command public confidence," Miliband said. "I'm going to meet Sir Ian Kennedy to tell him why I think this is wrong. I'm going to tell him why he has to think again. But I'm not going to let the matter rest there. I'm looking at all the options available to us with one purpose in mind – that this rise does not go ahead."

The issue of MPs' pay, a thorny issue at the best of times, has become a more highly charged political problem because nearly all public-sector workers, including nurses and teachers, have been asked to accept pay rises of less than 1% a year.

While many politicians say privately that their pay has been ignored for many years and led to the expenses scandal, most also agree that the public will not support a one-off increase if austerity measures are in place.

While many backbenchers are privately keen to accept a rise, some MPs are considering donating their rises to charity if a pay rise is forced on them. That, however, would require a degree of independent checking and transparency.

In a survey of all MPs by the Daily Telegraph, 45 politicians replied to say they would reject a pay rise, while just one, Charles Walker, MP for Broxbourne, said he would accept it.