Barker joined Sotheby’s in 1994 moving to the Contemporary Art department in 2001, rising to Chairman, Sotheby’s Europe, Senior International Specialist in 2016. He is a key figure on the rostrum at the major auctions in both London and New York.
In 2004, he oversaw the market-defining sale of the contents of Damien Hirst’s restaurant Pharmacy: “As the sale started it was clear we were definitely on to something… The sale had an estimate of around £3 million and it made £11 million with everything sold. Importantly it established a bond of trust between Sotheby’s and Hirst.” Five years later, he brought works to auction directly from the artist’s studio for the landmark Hirst sale Beautiful Inside My Head Forever, which achieved £111.5 million and established a world record for a single-artist sale. That same year he led the $40 million (RED) Auction, a major sale arranged by Bono and Damien Hirst to raise money for the United Nations Foundation to support HIV/AIDS relief programmes in Africa.
Barker has played a pivotal role in the growth of the global market for post-war British art, including for Bacon, Freud and the London school. The many exceptional results and records for British artists orchestrated by Barker include the 2015 sale of Lucian Freud’s postcard-sized painting Four Eggs on a Plate. Estimated at £100,000–150,000, it sold for around £1 million, almost ten times the painting’s low estimate. The same sale saw a similar margin of increase as a new auction record for any work on paper by Frank Auerbach was set with an early portrait of his cousin Gerda, Head of Gerda Boehm, from 1961 soaring to £2.2 million. Most recently, in May 2017, he hammered down Jean-Michel Basquiat's Untitled, 1982 for $110.5 million – a new auction record for a work by an American artist.
In November 2016, Barker led the landmark Bowie/Collector auction in London, which was 100% sold, totalling £32.9 million and attracting 1,750 bidders, and in September 2017 will be on the podium for Shake It Up: Works from the Mario Testino Collection.