Henry Urmston Willink was born in Liverpool in March 1894. He was educated at Eton College and Trinity College, Cambridge. Before he could take his Cambridge degree he volunteered for service in the Royal Field Artillery during World War One, and gained the Military Cross, the Croix de Guerre, and was mention in dispatches. He was called to the bar (Inner Temple) in 1920, became a KC in 1935 and a Bencher of the Inner Temple in 1942.

After unsuccessfully contesting the Ipswich by-election in 1938, he was elected as an MP after winning the Croydon North by-election in June 1940. Until November 1943 he served as Special Commissioner for the Homeless in London and was then Minister of Health from 1943-5. He was made a Privy Councillor in 1943. After suffering from a period of ill health he was appointed Master of Magdalene College, Cambridge, with effect from January 1949, and resigned his parliamentary seat at the end of 1948.

On his retirement as Master of Magdalene in 1966 he was awarded an Honorary Fellowship of the College. During his time as Master he had served as Vice-Chancellor of Cambridge University (1953–5). He was also a fellow of Eton College (1946–56), and Dean of the Court of Arches (1955–69). Willink chaired the Royal Commission on Betting, Lotteries, and Gaming (1949–51), a Committee on Medical Manpower (1955), and a Royal commission on the Police (1961/1962).

Willink was created a baronet in July 1957. He died in January 1973.