The government is planning to introduce directly elected crime and policing representatives on police authorities.
But LGA chairman Margaret Eaton has claimed this will lead to “buck-passing and blame-shifting”.
“In the light of the Metropolitan Commissioner’s departure, the current proposals in the policing green paper need to be studied more than ever with a fine tooth comb,“ she said.
“Councillors from all political parties have serious concerns about the proposals being made to introduce directly elected representatives at the local level. This competing mandate will make it more difficult for the public to understand who is actually responsible for policing.”
Sir Ian stepped down after being told he should go by London mayor Boris Johnson.
“Without the mayor’s backing I felt I could not stay in the job,” he said.
Mayor Johnson has indicated he will not replace Sir Ian until a Tory government is in place. Len Duvall, leader of the Labour group on the London Assembly, called for Sir Ian’s successor to be appointed swiftly.
“The Met must not be allowed to drift without firm leadership and the appointment of Sir Ian's replacement must, as with previous appointments, be made totally on merit; not on party political bias,” he said.