The mayoral elections are being postponed until 2018 so that the Sheffield city region (SCR) can consult the public on whether Chesterfield in Derbyshire should join the combined authority, along with Bassetlaw in Nottinghamshire.

Momentum is building behind calls for the SCR proposal to be scrapped in favour of a whole-Yorkshire deal. With more than 5 million residents, the four counties of Yorkshire have a bigger population than Scotland and a GDP double that of Wales.

Caroline Flint, the Labour MP for the Don Valley, said a Yorkshire-wide deal should be explored. “It’s disappointing that the deal has fallen through but maybe there is an opportunity to reflect on whether there is another way forward,” she said.

“Maybe there is a regional way to bring the whole of Yorkshire and the Humber together because if we were given the powers through devolution I think we could do a great job. With 5 million people it would be amazing the things we could do. There is nothing stronger than the Yorkshire brand – it’s one of the best things we have to promote our region.”

In October 2015 the Sheffield city region became the second combined authority to sign a devolution deal with the then chancellor, George Osborne, as part of his dream to build a “northern powerhouse” to rival London and the south-east.

Under the terms of the agreement, South Yorkshire was to elect its own mayor this May, along with Greater Manchester, Tees Valley, the West Midlands, the west of England and the Liverpool city region.

The former sports minister Richard Caborn and the Barnsley council leader, Stephen Houghton, had been expected to contest the Labour nomination for South Yorkshire mayor.

After the SCR officially postponed the mayoral elections on Thursday, Ros Jones, the mayor of Doncaster, and Houghton issued a joint statement saying they owed it to residents to “work with colleagues to explore this new Yorkshire-wide option, to ensure we give all potential devolution solutions proper consideration so that residents can be fully informed when being asked to participate in consultation over the summer months”.

Conservative MPs and councillors in Yorkshire have long favoured a whole-Yorkshire deal, reasoning that their party would then have a better shot at winning a mayoral election. The idea has been strongly resisted, particularly by Labour leaders in West Yorkshire, who caused David Cameron to once remark: “We just thought people in Yorkshire hated everyone else; we didn’t realise they hated each other so much.”

In September last year the five Labour leaders of West Yorkshire’s councils – Leeds, Bradford, Wakefield, Calderdale and Kirklees – reluctantly agreed to follow Greater Manchester’s lead and accept the imposition of an elected mayor in return for more power. Their proposed Leeds city region would have included cooperation with York, Selby, Craven and Harrogate in North Yorkshire.

But the deal was stymied by Tories including Kevin Hollinrake, the MP for Thirsk and Malton, who told the Guardian last year that when he was councillor he had lobbied Osborne and the then local government minister, Greg Clark, to reject the West Yorkshire deal. He denied his objections were politically motivated, saying he thought the proposed geography was “very counterproductive and ill-thought-out” and would put his rural constituency at a disadvantage.

“The reason I was concerned is that the West Yorkshire deal encompassed York and Harrogate, and as a representative for a rural North Yorkshire seat it would cause significant problems to have the key towns and city within our economy included and us left outside,” he said.

Hollinrake and other Conservatives prefer the idea of a Greater Yorkshire devolution deal. “It’s in the economic best interests of my region. This isn’t political. According to our calculations, if there were a mayor of Greater Yorkshire it’s very evenly balanced as to whether they are Labour or Conservative or indeed independent,” he said.