Glyn was a younger son of George Glyn, 1st Baron Wolverton, and his first wife Marianne, daughter of Pascoe Grenfell. George Glyn, 2nd Baron Wolverton, and Vice-Admiral the Hon. Henry Carr Glyn were his elder brothers while the Right Reverend the Hon. Edward Glyn, Bishop of Peterborough, was his younger brother. He entered Parliament for Shaftesbury in the 1880 general election, a seat he held until 1885, when the constituency was abolished.
Glyn married Fanny, daughter of Adolphe Marescaux, in 1868. He died in February 1916, aged 80.