From the Wikipedia page 
Borough Road railway station was a railway station in Borough Road, Southwark, south London, England, on the London, Chatham and Dover Railway, which was first opened in 1864 on the railway's City Branch, and which crossed the River Thames and ran up through Blackfriars to terminate in the City of London. From 1885 following the closure to passengers of Blackfriars Bridge Station, Borough Road was the first stop out of central London for trains heading south from Blackfriars railway station.
Ultimately, Borough Road was an early victim of competition from the Northern Line when Borough tube station opened in 1890. Passenger numbers dwindled and the station closed in 1907. In 1916 two other stations on the line to the south, Walworth Road and Camberwell, were also closed. Today the trains run straight through from Blackfriars to either Loughborough Junction or Denmark Hill, stopping only at Elephant and Castle.
There have been recent calls for a new station on the line, though it would be unlikely to be at Borough Road.