A City Hall statement released on Monday said the mayor had a provisional agreement with 14 London boroughs to deliver over 16,750 homes.
It said that the remaining 19 boroughs had “identified” sites for a further 20,500 affordable homes.
However, London Assembly officials refused to publish any breakdown of individual targets for each borough.
He added: “Boris needs to put his money where his mouth is. These targets are meaningless if Boris does secure the money from the Homes & Communities Agency.”
Sir Robin said: “We are meeting with GLA officials to negotiate a realistic and, more importantly, deliverable target based on the current economic climate and our vision for a mixed and sustainable community.”
Mr Johnson had originally pledged in his manifesto that he would build 50,000 affordable homes over the next three years.