The comments come after the authority decided to sell three council-owned car parks in October to address a £27 million budget gap predicted for next year.
Council officers said the car parks based on Abery Street, Old Dover Road and Charlton Village were not well used and the land they were on could be attractive for property developers.
Conservative Councillor Matt Hartley said at a Greenwich Council meeting on December 4 that local businesses and residents were concerned about the effect the sale of such car parks would have on their areas.
Cllr Hartley said: “I spoke to Keith and his 94-year-old mum, who’s disabled and a Blue Badge holder, and Keith told me that without Old Dover Road car park it is not going to be feasible for him to bring his 94-year-old mum to the caffs and shops at the [Royal] Standard.
“He told me it’s one of the few things that brings her any quality of life at all.”
He asked the council leader to request officers to conduct economic and quality impact assessments to determine the effect of removing such car parks.
Labour Councillor Anthony Okereke, leader of the council, said in response that he recognised the concerns of locals and that the decision to sell the car parks was based on surveys indicating low usage and ongoing operational costs.
Council documents from earlier in the year claimed the installation of cameras in two of the car parks had generated additional costs for Greenwich Council.
Cllr Okereke added that the sale was not determining the future use of the sites and any changes would require planning permission. Officers had also previously confirmed that the car parks would remain open until sales were agreed.
He added: “It’s worth noting that there is also on-street parking on the road as well. From our assessments of the car park, the use has not been that high. But let’s not jump ahead, let’s not decide what could be there, we don’t know yet.
“We have not tested the market in terms of what will come forward in that area and we will continue to listen and engage.”