Buxton was born on 18 November 1822 in Cromer, Norfolk, the third son of Sir Thomas Buxton, 1st Baronet, a notable brewer, MP and social reformer, and followed in his father's footsteps, becoming a partner in the brewery of Truman, Hanbury, Buxton, & Co in Brick Lane, Spitalfields, London, and then an MP. He served as Liberal MP for Newport, Isle of Wight (1857–1859), Maidstone (1859–1865) and East Surrey (1865–1871). His son Sydney Buxton was also an MP and governor of South Africa.