The board of Foxtons has come under pressure from 10% of its shareholders to sell the business.
Milkwood Capital, which owns about 4%, is the latest shareholder to demand a sale of the estate agency.
It follows pressure from Canadian investor Converium Capital, which has been lobbying for Foxtons to carry out a strategic review over the past 18 months.
In 2014, Foxtons floated at 230p a share. On Friday shares closed at 40.5p.
