The ruling Conservative group voted to press ahead with the contentious 380-space project in Station Road West close to Canterbury West train station.
Eight Lib Dem and Labour councillors supported the petition and are poised to use hostility towards the car park as a key element of their campaigns in this year’s local election in May.
The petition and vote came at the meeting of the full council in the Guildhall last night (Thursday, January 10).
Earlier in the day the authority released details of its plan for an integrated transport hub in the area around the station.
It includes an area for taxis to pick up and drop off from, more ticket machines and barriers and an area designated “increased space for transport interchange” for buses.
Cllr Ben Fitter-Harding, chairman of the regeneration and property committee, said: “This is our collaborative idea of how the area could look in the future as the multi-storey car park and additional spaces it brings unlocks land around the station, allowing its function as a transport hub to be enhanced.
“Between us we will need to draw up more detailed plans, and decide how the improvements will be funded.
“We will work hard with our partners to deliver this plan and our map provides all those who are involved with something to aspire to.”
At the end of last year, the council allowed preparatory sewage work to take place in Station Road West ahead of construction of the car park.
More work is currently taking place and the building of the car park is due to start in February.