After graduating in philosophy from the University of Warwick, he became editor and press officer for the Campaign for Nuclear Disarmament, and was a member of The Leveller magazine collective. Subsequently he joined The Times, then The Sunday Times, first as a business news subeditor and then as a staff news reporter and feature writer. In the 1980s, under then Sunday Times editor Andrew Neil, Deer was the UK's first social affairs correspondent, and between 1990 and 1992 reported from the United States.
In 1986, one of Deer's early investigations exposed research by British scientist Professor Michael Briggs at Deakin University, Australia into the safety of the contraceptive pill. Deer's reports revealed that numerous of Briggs's studies were fabricated so as to give a positive profile for the products' cardiovascular safety. The research was largely financed by the German drug company Schering AG.
In 1994, his investigation of The Wellcome Trust led to the withdrawal in the UK of the blockbuster antibiotic, Septrin (also sold under the name Bactrim) and the sale by the Wellcome Trust of its drug company subsidiary.
In 2005, the withdrawal of the painkiller Vioxx was followed by an investigation by Deer into the people responsible for the drug's introduction.
In 2006, Deer's Dispatches documentary "The drug trial that went wrong", investigated the experimental monoclonal antibody TGN1412. It was nominated for a Royal Television Society journalism award.
In 2008, the media psychiatrist, Raj Persaud, was suspended from practising medicine and resigned his academic position after being found guilty of plagiarism following an investigation by Deer.
In a series of reports between 2004 and 2010, Deer investigated concerns over the MMR vaccine that arose with the publication in 1998 of a research paper in the medical journal The Lancet written by Andrew Wakefield, and his colleagues. Deer revealed that Wakefield had multiple undeclared conflicts of interest, had manipulated evidence, and was responsible for what the BMJ later called "an elaborate fraud".
Deer's investigation led to the longest-ever inquiry by the UK General Medical Council (GMC). In January 2010, the GMC judged Wakefield to be "dishonest", "unethical" and "callous", and on 24 May 2010, Wakefield was removed ("struck off") from the UK medical register. Responding to Deer's findings, The Lancet partially retracted Wakefield's research in February 2004, and fully retracted it in February 2010 following the GMC findings. In 2011, Deer published his findings in the BMJ with an endorsement by the editors.
On 18 November 2004, UK Channel 4's Dispatches series broadcast Deer's television documentary: "MMR: What they didn't tell you". Television critic Nancy Banks-Smith wrote in The Guardian: "After a year of rebuffs, Deer ran Dr Wakefield to ground at an Indianapolis conference on autism. The camera took a bit of a buffet and Dr Wakefield left with Deer following, shouting: 'We have very important questions to ask you about your research and your commercial ambitions, sir! Will you stand your ground and answer?' If this was hounding, and it was, Dr Wakefield had only himself to blame for running away".
In response to the documentary, Wakefield initiated a libel suit against Deer. The case was later dropped and Wakefield became liable for the costs incurred by Deer and the other defendants.
In January 2012, Wakefield sued Deer and the British Medical Journal, this time in Texas, but the case was thrown out in both district and appeals courts, with Wakefield again ordered to pay costs.
In October 2014, in an article published in The Sunday Times, Deer reported on a ruling from the Court of Protection, then recently made public but with the identities of the parties redacted. In the ruling, Justice Baker wrote, "The critical facts established in this case can be summarised as follows. M has autistic disorder. There is no evidence that his autism was caused by the MMR vaccination. His parents’ account of an adverse reaction to that vaccination is fabricated."
In July 2015, Deer gave a lecture at The Amazing Meeting titled "Vaccines: The Vanishing Victims".
Working for The Times and The Sunday Times Deer received several awards, including two British Press Awards for his Sunday Times investigations.
Following his first British Press Award in 1999, in February 2011 he was nominated for two more, in the categories of news reporter of the year and specialist journalist of the year, the latter of which he won on 5 April 2011.
In October 2011, Deer won the annual HealthWatch award, previously awarded to Sir Iain Chalmers, Professor David Colquhoun, and other prominent British medical campaigners.
Deer was the 2009 Susan B Meister lecturer in child health policy at the University of Michigan, and the 2012 Distinguished Lecturer in Life Sciences at the University of Wisconsin, La Crosse.
On November 17, 2016 Deer was awarded the honorary degree of Doctor of Letters (D Litt Hon) by York St John University.