After doing National Service and studying at Wadham College, Oxford University, where he edited the Cherwell newspaper, Esser began his career as a reporter with the Daily Express and Daily Sketch in 1957. He edited the Express' "Hickey" column, and gave both Nigel Dempster and Paul Dacre their first jobs on a national newspaper. By 1969, he was the newspaper's New York editor, and was the first British journalist to interview the Apollo 11 astronauts.
He later became consultant editor of the London Evening News, before in 1985 returning to the Daily Express. In 1986, he became editor of the Sunday Express, a post he held until 1989. A great supporter and friend of Margaret Thatcher, Esser was due to receive a knighthood in 1990 but declined the honour on the grounds that it was not appropriate for a serving editor to accept it.
Esser moved to the Daily Mail in 1991, where he introduced an arts and entertainment supplement, published on Fridays. He subsequently became the paper's Executive Managing Editor and oversaw the launch of its website MailOnline.
Esser published three books, The Hot Potato (1969), The Paper Chase (1971), and Crusaders In Chains (2015).
He was married to Shirley Clough and had 4 children with her. After an accident in 1972 while on holiday Shirley died and Robin was left a widower. He Met Tui France his second wife and remarried in 1981 and went on to have 2 more children with her. He died a father of 6, a grandfather of 10 and a great grandfather of 4.