Born in Eton, Berkshire, Berry was the sixth and youngest son of newspaper magnate James Berry, 1st Viscount Kemsley, and his wife Mary (née Holmes).
He married firstly, at Westminster in 1954, the Hon. Mary Cynthia Roche (born 1934), a daughter of 4th Baron Fermoy. Mary's sister, Frances, married John Spencer, 8th Earl Spencer and so Anthony Berry was an uncle of Diana, Princess of Wales and great-uncle of The Duke of Cambridge (second in line to the throne).
Sir Anthony and his wife Mary had four children: Alexandra Mary (born 1955), Antonia Ruth and Joanna Cynthia (twins, born 1957), and Edward Anthony Morys (born 1960). They divorced in 1966.
He then married Sarah Clifford-Turner at Chelsea in 1966 and had two more children: George (born 1967), and Sasha Jane (born 1969).
In 1962 he was appointed High Sheriff of Glamorgan.
He was elected as Conservative MP for Southgate (later Enfield Southgate) at the 1964 general election, and served in Margaret Thatcher's government after the Conservatives won the general election in 1979. He served as Vice-Chamberlain of the Household between 1979 and 1981, Comptroller of the Household from 1981 to 1983 and was appointed Treasurer of the Household in 1983. He was knighted in December 1983. At the time of his death he was Deputy Chief Whip in Thatcher's government.
On 12 October 1984, Berry was killed in the Brighton hotel bombing, when a bomb was planted in the Grand Hotel in Brighton during the Conservative Party's conference. He was 59. He was survived by his wife, Lady Berry, who was injured in the blast.
His death in office triggered a by-election in Enfield Southgate, which was won by Michael Portillo.
In September 1986, Patrick Magee who carried out the bombing, received eight life sentences, but was released from prison in 1999 under the terms of the Good Friday agreement.
Since Magee's release, Berry's daughter, Jo Berry (a mother of three living in North West England) has received attention for her series of controversial meetings with the Brighton bomber, as part of her quest to come to terms with the bombing and, in her own words, "to bring something positive out of it". Some of their discussions were filmed for an Everyman programme, shown on BBC2 on Thursday 13 December 2001. She has received some criticism from other families of IRA victims for these meetings.
A ceremony was held in Berry's Enfield Southgate constituency on 12 October 2009, the 25th anniversary of the bombing, at which his widow (wife of Lord Donoughue) and her daughter Sasha unveiled a plaque in his honour at the newly renamed Sir Anthony Berry House in Chaseville Parade, Winchmore Hill.