Dickinson was the son of Sebastian Stewart Dickinson, Member of Parliament for Strud. He was Member of Parliament for St. Pancras North from 1906 to 1918 and was an assiduous supporter of women's suffrage, promoting a number of measures in Parliament to get the vote for women. Dickinson was made a Privy Counsellor in 1914 and in 1930 he was raised to the peerage as Baron Dickinson, of Painswick in the County of Gloucester.
He was later secretary-general of the World Alliance for International Friendship, and from 1931 chairman of its International Council.
He married Elizabeth, daughter of General Sir Richard John Meade, in 1891. They had three children, one of whom was Frances Joan Dickinson, Baroness Northchurch. Lord Dickinson died in May 1943, aged 84, and was succeeded in the barony by his grandson Richard, his only son the Hon. Richard Sebastian Willoughby Dickinson having predeceased him.