Up to a million new jobs could be created across England if more power was devolved to cities, research by town hall leaders suggests.
English cities are falling behind London, the LGA warns
Only London is ranked in the top 30 of Europe's wealthiest urban centres, the Local Government Association said.
It said increased control in areas like housing, planning and transport would enable regional cities to catch up.
The government said cities have been recovering after years of decline but it was looking to devolve more powers.
The LGA report Prosperous Communities, which is backed by all the three main parties at local level, calls for a shift in powers and funding.
Bristol is ranked 34 in the wealthiest urban centres listing, the LGA noted.
But it said former economic powerhouses such as Liverpool and Birmingham are underperforming their continental peers.
It urged ministers to look to the example of cities in the EU and US which have benefited from devolved powers.
The report argues that the economy functions more at the level of the city and its surrounding commuting belts than regionally or nationally.
"We have a great global city in London. But other places in Britain, once world-beaters, have fallen behind," said LGA chairman Sandy Bruce-Lockhart.
"If England's cities are to close the gap with other countries, let alone with London, their productivity and competitiveness need to stride forwards.
"Local structural improvements in the economy can only come from local decision-making."
Local Government Minister Angela Smith said a White Paper lists proposals to support cities to accelerate economic growth and recognises the benefits of devolving more powers.
"As a result of sustained economic growth and rising investment, our major cities have recovered after years of decline and are once again successful places to live and work," she said.
"However, we agree with the LGA there is still more to do."