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Raised in the West Midlands and educated at Solihull School in Solihull, Millichip played for the third team of West Bromwich Albion in the years before World War II. During the war, he served in North Africa, Canada, Sicily and Italy, rising from an enlisted man to the rank of captain.
On demobilisation in 1945, he returned to his solicitor's practice and became a director of West Bromwich Albion. He took on the role of chairman in 1974 when the club was failing to make progress in the Second Division under manager Don Howe. Under Millichip's chairmanship, the club re-established itself in the First Division and recruited talented and energetic manager Ron Atkinson, building a team that was among the most exciting in English football circa 1980. It was during this time that West Bromwich Albion were the first club to field simultaneously three black players. The young talented three, Brendon Batson, Laurie Cunningham and Cyrille Regis, made a huge impression and became known as the Three Degrees, in comparison to the vocal trio of the same name.
In 1981, Millichip was elected chairman of The Football Association at the start of a period during which the English game was to be rocked by a succession of crises including the Heysel Stadium disaster, the Hillsborough disaster, growing problems of hooliganism, the national team's repeated international failure and the founding of the Premier League. His vacillation over the appointment of Terry Venables as manager of the national team, when the latter was under investigation and criticism for his business dealings, led journalist Brian Glanville to dub him Bert the inert.
In 1950 he married Joan Brown. They had a son and a daughter. His son, Peter Millichip, who also followed his father into law, was also an ardent fan of West Bromwich Albion. He was a close friend of Sir Bobby Robson, and as Sir Bobby entered his final years, they worked together to establish the Sir Bobby Robson Football Academy, in Birmingham.
- "12 New Honours". FIFA. Retrieved 24 March 2017.