The council said around 57,000 households had signed up to the scheme, about a third of households in the area.
It said it hoped the charge would bring in £4m.
Councillor Mick Warren, who leads the council’s environment and communities committee, said: “We don’t want to charge people for this, it’s a necessity.
“It’s a non-statutory service. It’s something that is very popular with residents,” he said.
“It’s not just the collection of green waste, the whole service is under financial pressure.”
Mr Warren added he expected numbers to increase to around 90,000 by the spring and summer months.
