Henri Murison is chief executive of the Northern Powerhouse Partnership, a business-led think tank and advocacy group for the North of England which fosters collaboration between local and national government.
He said the chess boards “summed up just how tokenistic levelling up had become”.
Mr Murison added: “It shows the misunderstanding the prime minister has about how local government works, because his job in central government is to give local government enough money to pick its own priorities, not to throw sweeties at the provinces.
“If there’s money to spend, it should be spent on what local people want and need the most. Now, nothing locally happens without some sort of top down initiative.
“This approach of taking big decisions in Whitehall and micro-managing the small decisions is a symptom of a broken relationship between central and local government.”
A government spokesman said: “We’re spending £15 billion in levelling up funding to spread opportunity, regenerate areas most in need and enhance cherished community spaces.
“Community chess tables will improve local green spaces, encourage more to play chess together and inspire the next generation of players.”
