Barking and Dagenham is the first Labour-run London council to object to Sadiq Khan's ULEZ expansion plans.
On Twitter Mr Rodwell wrote: "We have made the case to TfL that we need a much more comprehensive and generous scrappage and support scheme for outer London, and a greater lead-in time for people to take advantage of any schemes given the cost-of-living pressures facing people at the moment."
The BBC has contacted other London Labour councils about the matter, with some privately expressing similar concerns.A council spokesperson said: "As a council, we remain committed to improving air quality to ensure Redbridge is a healthy environment for local people, now and for generations to come.
Three Liberal Democrat councils - Sutton, Kingston and Richmond - are calling for a delay and measures to mitigate the effects, such as by providing more public transport, more money to compensate motorists disposing of vehicles and more investment in local "active" transport alternatives.
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