But Sir Peter now says he needs more powers. In particular, he has economic regeneration and transport in his sights... and even policing.

He's been encouraged by sympathetic noises from Downing Street. So BBC TV's Sunday Politics in the East Midlands took Sir Peter to Brussels.

We wanted to find out the powers he would have if he swapped running Leicester for Brussels.

He summed up some of the limitations of the present mayoral set-up in England: "The mayor can provide some co-ordination and influence, but doesn't actually have the power to make things happen."

In the historic heart of Brussels city centre, the Grand Place, we met my friend Jef Baeck.

"The mayor of Brussels has large powers," he told us.

"He has responsibility for the police and power over all the other activities to organise a city. Commercial activities. Even health. So I would say he's like a local king!"

The city's mayor is in fact a rugby-loving socialist. Freddy Thielemans has been running Brussels for 12 years. He says: "A mayor is two things. He's chair of a city but he's also the identity of the city. That's very important"

"It's not so much about power but a conversation with the people who will be doing it for you and the city. A mayor is two things: he's chair of a city but he's also the identity of the city. That's very important," says Mr Thielemans.

Independent funding

Another difference is the local source of revenue for the city's treasury.

"We have commercial taxes that are local. We have restaurant taxes and we get revenue from any event on our territory. There's also parking tax. This revenue is important to us because it gives us independence from the state," he added.

Mr Thielemans faces elections this autumn. Public transport is a big issue. Would Brussels embrace an initiative from another city with an elected mayor, the congestion charge of London?

"We are looking at it," he told me.

"We want to deeply change what's occurring in the city. We need more backing for public transport and making the city easier for walkers and cyclists. That's the future demand."

Sir Peter was taken to see an award-winning regeneration project in a former run-down area of the city. Sir Peter said "It is frustrating that in England there are many agencies that control the sites that require regenerating. Powers of compulsory purchase are also limited"

There are community facilities and a children's play centre. The scheme cost several million euros and was promoted by Mayor Thielemans.

"I was determined that Brussels wouldn't become a city where just the rich live in the centre and the poor are on the outside," he told me.

With a reference to last summer's riots in England, he added: "We want more of a socially mixed city because without that we get the sort of problems we have seen in countries close by."

La Savonnerie Heymans in the rue d'Anderlecht was the type of regeneration scheme which caught the eye of Sir Peter.

"The mayor actually has control of the site itself in Brussels, so you are not waiting around for someone else to do something to the site.

"It is frustrating that in England there are many agencies that control the sites that require regenerating. Powers of compulsory purchase are also limited," he said.

So after his visit to meet Mayor Thielemans, Sir Peter is taking a message to Downing Street.

"There are additional powers that need to come to the mayor of Leicester and other mayors. But it's not just about powers. It's also about providing leadership and to that extent the role of the mayor of Brussels and the role of mayor of a UK city are very similar."

Sir Peter hopes to persuade David Cameron that Brussels has the answer for English city mayors.