Roberts was born on 17 March 1965 in Winchester, Hampshire, UK. He was educated at Winchester College, which is an all-boys public school in Winchester.

He studied law at Selwyn College, Cambridge and graduated from the University of Cambridge with a Bachelor of Arts (BA) degree in 1988; as per tradition, his BA was promoted to a Master of Arts (MA (Cantab)) degree in 1991. In 1987, he was President of the Cambridge Inter-Collegiate Christian Union.

After graduation, he spent a short time in student ministry in South Africa. Roberts then moved to Oxford and in 1989 entered Wycliffe Hall, an Anglican theological college. There, he studied theology and undertook training for ordained ministry.

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