There is no service between Finchley Road and Waterloo and there are severe delays on the rest of the line.
Engineers are currently fixing a signal failure at Bond Street.
Tickets are being accepted on London Buses, the Mildmay line, DLR, Elizabeth line, C2C, Southeastern and Thameslink services.
It comes as Storm Goretti continues to batter the UK with tens of thousands of Britons across the country facing widespread travel disruption.
