The Lewisham project depended on Landsec gaining control of a former Citibank tower next to the shopping centre. Local news site The Greenwich Wire first reported that the council had decided to drop the plans.
But after the Greens took control of the council in May, Mr Shrivastava said he would not help the developer unless it added more affordable housing.
Of the 1,744 homes planned for the redevelopment, 98 would have been offered to social tenants for rent.
A Landsec spokesman said: “Higher interest rates, increased construction costs and more complex regulations have made development in London increasingly challenging.
“Recent statements from Lewisham Council also make clear that the administration is not able to support the next phase of land assembly needed to unlock delivery without a significant increase in affordable housing. This would require material changes to the masterplan which would prolong the programme.”
The spokesman added: “This position, combined with the exceptionally challenging economic conditions, means that we no longer see a sufficiently certain route to delivery.”
Mr Shrivastava said his administration was “laser focused on delivering genuinely affordable housing”. He added: “I’ve consistently said the level of social rent homes in this scheme needed to increase.”
However, he admitted that conditions for major projects, such as Lewisham, were “simply not favourable right now” and that ministers needed to enact “urgent reform” to revive construction.