Williamson was born in Camberwell, London (GB) on 12 January 1948, and grew up in Bermondsey, London. His family later moved to Dartford, Kent, where he completed his education in 1966. He spent the majority of his career working for the British government before joining EMBL in 2001, from which he retired in December 2015.
As a parting gift to EMBL, he offered EMBL a large statue of the letter G, located at EMBL in Heidelberg. Alongside the initials of the Advanced Training Centre (ATC), the G represents guanine when A, T and C stand for adenine, thymine and cytosine respectively, forming the four nucleobases of DNA.