Clean Air Zone Framework
Published in May 2017, this is the UK Government response to the problems of Air Pollution.
It effectively removes responsibility for Air Quality Management Areas from Central Government and passes responsibility to Local Authorities.
Babergh District Council is ultimately responsible for lessening pollution in Cross Street, though without a Highways responsibility it must work with Suffolk County Council to deliver a solution.
It's a long read so a separate Alternative Solution article will precis the actions a Local Authority can take.