The National League South side have been playing at Champion Hill since 1912.
They ran into trouble in recent years and were forced to share at Imperial Fields, Tooting’s ground, for several months.
But they returned mid-way through last season and gates were in excess of 2,000 for most matches.
But now they see their future away from their long-term home.
“The club are pleased to announce that the application for a new stadium has been submitted,” a statement read.
“The club are pleased that after our successful return to Champion Hill and extensive consultation with fans, local residents and community groups, a planning application for a new stadium has been submitted to The London Borough of Southwark.
“The club plans to announce an open public meeting ASAP. Please check the website and social media channels for updates.”