Ministers will be expected to justify why powers should remain in Whitehall rather than being devolved, under a “local first” principle being developed by No 10 North in Manchester, with full details set to be published in a policy paper on the same date as the autumn budget.

The government is also working out the details of an equalisation system to ensure areas where less tax is collected continue to receive financial support.

The reforms come after a policy blitz during Burnham’s first two weeks in Downing Street, with announcements on the cost of living followed by a speech on his plan to overhaul social care.

Tracy Brabin, the Labour mayor of West Yorkshire, said that giving regions like hers a proportion of income tax would mean “people will be able to see and feel the real benefit of their hard work and where that money is going”.

However, Lord Houchen, the Conservative mayor for Tees Valley, said he would prefer the government to cut taxes and if handed a portion of income tax would create a new rebate scheme to give money back to local people.

“The prime minister has said he wants to alleviate the cost of living [crisis] and give people room to breathe – what better way to do that than allow them to keep more of their own money?” he told BBC Radio 4’s World at One programme.

“I think the prime minister and what this government is doing on fiscal devolution is a move in the right direction, but for it to be real devolution we’ve got to have local decision-making and choose what’s best for the people we represent.”

He said it was “not beyond the wit of man” for a regional authority to be able to set up a rebate system, adding it would not be “overly complicated” and would not be particularly controversial.

Burnham said the policy was “not about allowing mayors to become a sort of mini-chancellor” or “local home secretary”.

“This is a policy that is about growth and investment,” he told LBC, adding that he was “misunderstanding the purpose of this”.

“They don’t have to go for all of the things that are being suggested here, but, you know, we think these things will start to provide an answer to the low growth Britain has experienced over the last decade and more places start to see levels of growth that Greater Manchester has achieved.”

Additional reporting by Harry Farley, political correspondent, and James Gregory, political reporter.