National politicians who have made their names at Westminster could become the mayors of Britain’s great cities, David Cameron has predicted.

The Prime Minister said the creation of powerful city mayors would “renew” British politics.

He was speaking in Downing Street, at a reception to back the Government’s campaign to promote city mayors in the run-up to a referendum on May 3 which will decide whether Birmingham transforms the way it is governed.

He said: “I think a new generation of mayors in our cities will fundamentally enrich our politics as a whole.

“I look across the world and I see great politicians who run cities who then go on into national politics, and indeed you see national politicians go into city politics.

“I think that would enrich our political culture right here in the United Kingdom.”

In Birmingham, city MP Liam Byrne (Lab Hodge Hill), currently Labour’s shadow work and pensions secretary, is a national figure who is keen to stand as city mayor.

As well as his role in the Shadow Cabinet, he was appointed by Labour leader Ed Miliband to head the party’s policy review, following its 2010 General Election defeat.

Labour already has three potential candidates for mayor of Birmingham, with Edgbaston MP Gisela Stuart, former city MP Sion Simon and former council leader Sir Albert Bore all hoping to be selected.

Liberal Democrat MP John Hemming (Birmingham Yardley) has said he might stand for his party.

Birmingham City Council Leader Mike Whitby is in prime position to become the Conservative candidate. It remains to be seen whether any other Tories will come forward.

A major new collection of essays by leading think tank the Institute for Government has also highlighted the potential for politicians to cross over from national politics to running major cities.

The Institute, which has links to former Labour Minister Lord Adonis and senior Conservative Michael Heseltine, has published a series of essays in a booklet called What can Elected Mayors do for our Cities.

They include a paper by Guy Lodge, of the Institute of Public Policy Research, who said that city mayors would bridge the divide between national and local politics.

He wrote: “Mayors would not simply transform the look and feel of local politics but could have a transformative effect on Westminster too. Mayors who cut their teeth in Birmingham and elsewhere may later choose to enter national politics and would bring with them fresh perspectives that could make a big impact on national debate.

“And as we have seen in the case of Peter Soulsby and Sion Simon (two MPs who resigned their seats to fight for the mayoralty of Leicester and Birmingham respectively) the office of mayor might also attract national politicians back to their localities – a migration that is simply inconceivable under the current council leader model.

“In short, mayors in each of our major cities would represent a concrete move towards a more plural and layered polity.”

But a number of contributors to the booklet warned that city mayors will need powers over a wider “city region” in order to be effective.

So-called metro mayors would be able to influence housing, transport and economic growth while a mayor whose authority was limited to a city such as Birmingham might struggle, it was claimed.

Andrew Carter of the Centre for Cities, said city mayors should play a major role on regional bodies including chairing the integrated transport authority, such as West Midlands authority Centro.

He said: “City economies often stretch far beyond the boundaries of their core local authorities. To overcome this limitation, the option to introduce metro mayors should also be made available to all of England’s largest cities.”

Metro mayors should also co-chair local enterprise partnerships, which typically cross local authority boundaries, he said.

The Greater Birmingham and Solihull LEP covers Birmingham, Bromsgrove, Cannock Chase, East Staffordshire, Lichfield, Redditch, Solihull, Tamworth and Wyre Forest.

Metro mayors should also have the power to “develop a strategic spatial plan for the wider area, which local planning authorities must have regard to when developing or updating their local plans”, he said.

Ed Cox, Institute for Public Policy Research North warned that mayors must have real authority, including control over transport funding and “responsibility for commissioning local rail and bus services”.

But he added that metro mayors would have a higher profile and more authority than city mayors, “which enables stronger advocacy with central government, business and other interests.”

Powers a metro mayor should be given include “the ability to set a wide-ranging strategic spatial plan that extends across the city region or functional economic area and acts as the basis for all other local authority plans and to take decisions on all policy and planning applications that have a strategic significance for the wider economic development of the city region,” he said.

The Institute for Government also published the findings of polling which found that across the country, only 15 per cent of people, one in seven, believed they could name the leader of their local council - and only half of those actually knew the correct name when asked.

But 38 per cent said they would rather be governed by a mayor with 25 per cent backing the council leader model. Others said they did not know or did not care how their council was run.

David Cameron’s announcement that he plans to create a “cabinet of mayors” to meet him and other members of the Government has provided a boost to “yes” campaigners in Birmingham and other cities.

Cities Minister Greg Clark said: “A mayors Cabinet is a real opportunity for an elected mayor to represent their communities at the heart of Government and will ensure their city’s voice is heard right at the top.

"Mayors are a very good way of providing the strong, visible leadership that helps attract investment and have enormous potential to drive a city’s future prosperity.

“By coming together, sharing innovations and building relationships, city mayors will play an important role in ensuring their city lives up to its full potential.”

In Coventry, supporters of a mayor said the city risked being relegated to “third division status” if it failed to appoint a mayor.

The Prime Minister’s reception at Number 10, where he announced the cabinet plan, was attended by guests including Coventry campaigners Jon Gaunt, the radio personality, and businessman Darren Jones, who both back a mayor. The prestigious event was also attended by Coventry pop mogul Pete Waterman.

Mr Gaunt said: “I believe that great cities like Coventry need a mayor. We need a leader who is willing to fight like a dog for Coventry.”

The Coventry-born presenter, who has returned to the Midlands after pursuing his broadcasting career in London, would not be drawn on whether he plans to stand.

He said: “I firmly support the ‘yes’ campaign, and who knows. Many people want me to do it.

“What matters at the moment is that people vote ‘yes’, because Coventry needs change.”

The Government believes a “yes” vote is likely in at least four of the ten cities holding referendums on May 3, but believes other cities may follow if mayors are seen to be a success.

Ministers have high hopes that Birmingham will adopt a mayor, and as Britain’s largest local authority it will provide a model for other authorities to follow.

Meanwhile, the largest business organisation representing Asian companies has thrown its weight behind the “yes” campaign, arguing that an elected mayor for Birmingham will deliver a better deal for Asian businesses.

The Institute of Asian Businesses’ (IAB) president and executive committee are unanimously in favour of the introduction of an elected mayor and are urging member businesses to make sure they are registered to vote ahead of the referendum on May 3.

Nasir Awan, president of the IAB, said: “This is a positive move bringing the city into line with other major cities of the world where the mayor who is publicly elected works hard to promote the city nationally and internationally.

“Along with other benefits this would bring business and investment opportunities into the city benefitting the whole business community.”

Birmingham Chamber of Commerce is also backing a mayor.

The Government has ordered 10 major cities to hold referendums on creating a mayor on May 3.

Among those to decide will be Birmingham, Bradford, Bristol, Coventry, Leeds, Manchester, Newcastle-Upon-Tyne, Nottingham, Sheffield and Wakefield.

The list originally included Leicester and Liverpool, but councillors in both cities decided to move to a mayoral system without a referendum.