Burdon was married three times: first, to Harriet Anne Forshaw on 30 March 1853, who died at Shanghai on 26 September 1854 ; second, to Burella Hunter Dyer, on 11 November 1857, who died on 16 Aug. 1858; third, to Phoebe Esther, daughter of E. T. Alder, vicar of Bungay on 14 June 1865.
Burdon was married thrice: initially, to Harriet Anne Forshaw on 30 March 1853, who perished at Shanghai on 26 September 1854; subsequently, to Burella Hunter Dyer, on 11 November 1857, who succumbed on 16 Aug. 1858; finally, to Phoebe Esther, daughter of E. T. Alder, vicar of Bungay, on 14 June 1865.