Peterborough Litter Wombles was formed five years ago and now has about 500 active volunteers.
Machin said the group had collected more than 15,000 bags of litter since then, but claimed that was “only the tip of the iceberg”.
He said he was aware of funding challenges facing local authorities but added he would “love the council to do more”.
Stephen Eastman, founder of another local group called the Independent Review Committee on Debris, praised the latest initiative and said other parts of Peterborough would benefit from them.
Chris Wiggin, a councillor with a responsibility for the environment, said any new bins would be “subject to costs and installation requirements”.
“Alongside this we are focusing on developing educational activities, including organising regular litter picking activities at schools, to try and reduce the problem of litter occurring in the first place,” the Liberal Democrat councillor added.