He was educated at Eton (1837-1842), he won HRH the Prince Consort's Prize for French and Italian in 1842, and came second for French and German in 1841 and 1842, and was later a Fellow (1876-1880). He matriculated at Christ Church, Oxford 9 June 1843, (BA 1847, MA 1851), and was called to the Bar, Lincoln's Inn, in 1853.
He unsuccessfully contested East Sussex in 1852 and March 1857, but was elected for the constituency in April 1857. Dodson would hold this seat until 1874 and served as Chairman of Committees and Deputy Speaker of the House of Commons from February 1865 to April 1872. The latter year he was admitted to the Privy Council and in 1873 he was appointed Financial Secretary to the Treasury in the Liberal administration of William Gladstone, a post he held until the government fell the following year. In 1874 Dodson was elected to Parliament for Chester, and served as Chairman of the Public Accounts Committee from 1874 to 1876. In 1880 he was again elected for Chester and appointed President of the Local Government Board, with a seat in the cabinet, in Gladstone's second administration. According to the rules at the time, he was then forced to contest his constituency again. Dodson was duly elected, but shortly after the original election was declared void on petition. This caused him to seek re-election for another constituency. In July he was returned for Scarborough, a seat he would hold until 1884. Dodson remained President of the Local Government Board until 1882, and then served as Chancellor of the Duchy of Lancaster from 1882 to 1884. On 4 November 1884 he was raised to the peerage as Baron Monk Bretton, of Conyboro and Hurstpierpoint in the County of Sussex. Lord Monk Bretton later disagreed with Gladstone over Home Rule. He was also active in local politics, and served as the first Chairman of the East Sussex County Council from 1889 to 1892. He was a long serving director of the Rock Life Assurance Company and a member of the University, Reform, and Brooks's Clubs. Late in life he became concerned about the fate of the African elephant, whose salvation he mooted,in letters to The Times, could come through domestication.
Lord Monk Bretton married Florence, second daughter of William John Campion of Danny, Hurstpierpoint, Hassocks, in 1856. They had one son and three daughters. They lived at 6, Seamore Place in Mayfair, and at Conyboro', near Lewes, Sussex. In 1878 Edward Walford described Seamore Place: