The amended scheme was launched in April and offers council tenants a discount of up to £75,000 on the purchase price of their home, compared to a previous cap of £16,000.
Since the launch of the scheme Wandsworth Council has received more than 1,000 enquires for the scheme and the number of full applications has more than doubled. So far, the average discount offered to eligible Wandsworth council tenants is £72,000, the Council said.
"The tenants I've spoken to have been absolutely delighted with the changes and many are now in the process of applying for a mortgage," said Ravi Govindia of Wandsworth Council.
"In the weeks ahead we will be touring the borough to make sure all of our tenants are aware that this life changing scheme has been revived."
"The money raised through selling council homes will be used to build new affordable housing. Every home sold will be replaced," said Govindia.
"We are proud to be a home building council. Over the last ten years we have created more affordable homes than any other council in London and that experience will be invaluable," said Paul Ellis, Wandsworth executive member for housing.
However many councils are concerned that the money raised by the sale of homes will not be sufficient to replace them on a one for one basis with an affordable home.
"The Council is being forced to sell off the family silver. With these massive discounts I am not convinced we will get enough from the sale of each house to build another one," said Dr Joe McManners, an Oxford City Council board member for housing needs, according to a BBC report.