Named after Woodside House, built in Whetstone around 1840.
The house presumably took its name from some woods to the side. Joseph Baxendale, its builder, left it as a ladies' retirement home; the charity running it sold much of the grounds to developers, chiefly Henry Holden, who laid out roads on what he called the Woodside Park estate. The station opened in 1872 as Torrington Park and was renamed within a month, then again in 1882.