Councillor Mithra Cox said while Council's ability to intervene in the housing market was limited the scheme had not yet had a significant impact on housing affordability.
"It's an absolute drop in the ocean," she said. "A couple of housing units is really not going to touch the sides, but when you think about how much it costs to buy a house, it's difficult to stretch that money to a lot of people."
Ms Cox said without significant government interventions, which were out of reach of local governments, this would continue to be the case.
"Massively increasing the amount of social housing in the system is one of the key things that would improve housing affordability," she said. "That said, it's outside of council's remit to do that."