The only son of Norman, 1st Baron Birkett by his wife, Ruth (née Nilsson), Birkett attended Stowe before going up to Trinity College, Cambridge (MA).
On 10 February 1962, he succeeded his father as the 2nd Baron Birkett, a UK Peerage title created in 1958.
Birkett produced Sir Peter Hall's 1969 film A Midsummer Night's Dream and Peter Brook's pictures Marat/Sade (1967) and King Lear (1971), starring Paul Scofield. Executive producer of Brook's television mini-series The Mahabharata (1989), later he produced Harold Pinter's The Caretaker (1962) starring Alan Bates, Donald Pleasence and Robert Shaw, and directed by Clive Donner.
He was author of The Story of the Ring, a retelling of Wagner's operatic epic, published in 2009.
Birkett served as Deputy Director of The National Theatre between 1975 and 1977 (under Sir Peter Hall), subsequently being engaged as a consultant, before being appointed Director for Recreation and Arts at the Greater London Council from 1979 until its abolition in 1986.
He was executive director of the Royal Philharmonic Society, chairman of BAFTA as well as heading numerous other arts bodies. He also served as the chairman of Governors of the BRIT School for Performing Arts and Technology (1990–2001) and chairman of the Donatella Flick Conducting Competition (1990–2008).
A Freeman of the City of London, Birkett was admitted a liveryman of the Worshipful Company of Curriers, later serving as Master Currier (1975–76).
Having succeeded as Baron Birkett in 1962, later he took his seat on the Crossbenches of the Upper House. He was a leading proponent of a national lottery to provide extra funding for the Arts and proposed the idea in a speech before the House of Lords in 1988. Two years later he and Denis Vaughan formed the Lottery Promotion Company – solely advocating for legislation to establish a nonprofit-making, privately run lottery – a proposal that was adopted by PM John Major in 1994.
On 13 October 1960, Birkett married Mrs Junia Crawford (née Elliott); Lady Birkett died in 1973. In 1978 he married Gloria, daughter of Thomas Taylor, an industrialist, by whom he had a son, The Hon. Thomas Birkett (born 25 July 1982). Gloria, Lady Birkett (mother, by a previous marriage, of the actor Alexander Siddig), died on 10 February 2001.
Michael Birkett died in 2015 when the family title devolved upon the 3rd and present baron, his only child and heir, Tom Birkett, a cinematographer.