Clyde was born in the village of Dorney in the English county of Buckinghamshire and is the son of Lady Elizabeth Wellesley. Through his maternal line, Clyde is the great-great-great-grandson of Arthur Wellesley, 1st Duke of Wellington, and is a cousin of the current Duke of Wellington. Growing up, he was educated at two independent boarding schools in England: Ludgrove School, in Wokingham Without and Eton College in Eton. He also attended the University of Grenoble in Grenoble, France for one year. He would later go on to attend and graduate from the Central School of Speech and Drama, University of London where he studied acting. This is also where he met musical partner, Chad Stuart in 1960.