Ministers have tied the£1bn transport innovation fund (TIF) to the introduction of road pricing.
But the overwhelming ‘no’ vote in Greater Manchester’s December referendum has left the thinktank unconvinced that public opinion would allow road charging anywhere.
Centre for Cities said the funding should remain earmarked for transport, including new commuter rail links, better city buses and tram extensions.
After the next general election, the government should create a£4bn Urban Transport Investment Fund, using the TIF money to start this, the centre urged.
Centre for Cities director Dermot Finch said: “Cities like Manchester and Edinburgh have found congestion charging a tough sell.
“If there are no takers by the end of the year, the government should call it a day on its current road user charging push.”
Stephen Hughes, chief executive of Birmingham City Council, said his city and its neighbours has proposed an accelerated development zone to support transport projects.
"A fund such as that proposed by the Centre for Cities could be one way of providing the up front finance that would be required," Mr Hughes added.