Campaigners staged a protest outside Whiteleys shopping centre in Bayswater over its £1 billion redevelopment.
Proposals by architects Foster and Partners will see most of the Grade II listed building demolished apart from its facade. The new scheme includes a boutique hotel, cinema and space for retail units, as well as two towers featuring 103 luxury homes.
Critics say the plans offer no affordable housing and would block light to the buildings behind it. There are also concerns that digging for the basement levels could lead to subsidence or flooding.
Two online petitions urging a rethink of the development have now attracted more than 2000 signatures.