West Northamptonshire Council's cabinet approved the move to bring the former district authority area into line with Northampton and Daventry.
All three areas were absorbed into the new unitary authority last April.
But Cllr McCord, who now sits as an independent on the new council, told the meeting on Tuesday (November 9) the plans were 'pick-pocketing hard-working council tax payers who have few options.'
The former Conservative, who represents Deanshanger, added: "This Northamptonisation of West Northants continues apace.
"This is an attempt to mug-residents for £42 a year. It's pure profiteering and this level of charge is not necessary.
"It's just a way of getting an extra £800,000 from residents with nothing in return.
"Residents of South Northants are paying for and have paid for green waste to be disposed of as part of their council tax.
"This administration needs to stop treating those people as a cash point and start treating them with respect."
Cabinet approved a report recommending introducing the £42-a-year opt-in subscription service — dubbed a 'brown bin tax' by critics — across the Tory-run council area from next April.
That means the charge for Northampton residents will remain the same as it was when a borough council scheme was first introduced in 2020.
In the former Daventry District Council area, the cost has risen from £35. Last year's payment of £37 covered only ten months from June to April.
Cllr McCord also scolded the cabinet for 'ducking' any consultation process over introducing the charge.
He was backed by Towcester and Roade Tory councillor Maggie Clubley plus two Northampton members, LibDem Sally Beardsworth and Labour's Emma Roberts.
West Northants deputy leader, Adam Brown, admitted that 'as ward member for Bugbrooke, this is not a comfortable report to read.'
But he added: "We're not tinkering with the service. We're making a necessary and enforced harmonisation of the charge.
"We're not going a Northampton way we're going a West Northamptonshire way and its not helpful to start redrawing old boundaries that disappeared under reorganisation.
"We as members have a duty to serve in the best interests of all residents across West Northamptonshire."