Ravi Govindia has written to London's deputy mayor for transport calling for answers as to what is going on with the scheme.
The council set aside £27 million a decade ago to help fund the programme.
It would remove all through-traffic from Wandsworth High Street to help cut pollution and improve collision statistics.
There were 48 accidents in the three years to December 2019.
Transport for London originally said that work would start in 2017.
We’ve contacted TfL for comment.