In 1877, Burrows moved to London and joined the National Secular Society. He was a founder member of the Aristotelian Society in 1880, joined the Social and Political Education League and became Vice President of the Manhood Suffrage League. In 1881, he was a founder member of the Democratic Federation, and he became its treasurer in 1883.
Burrows supported the Federation's commitment to socialism in 1884, when it was renamed the Social Democratic Federation (SDF). He represented the group on the executive of the Law and Liberty League.
With Annie Besant, Burrows was a key organiser of the London matchgirls strike of 1888, and afterwards became the treasurer of the Union of Women Matchmakers. He also became a prominent member of the Rainbow Circle, the Theosophical Society, the International Arbitration and Peace Association and the International Arbitration League.
Burrows stood for Parliament unsuccessfully in the Haggerston by-election, 1908, and again in Haggerston in 1910. Disillusioned by his poor performance and the SDF's apparent commitment to militarism, he resigned from the organisation in 1911.