Adams was born in Byfield, Northamptonshire. His father was a railwayman, and grew up in a rural farming area in Northamptonshire. Adams had two older brothers, an older sister, and a younger brother.
Adams went to Byfield Council School, then his parents moved in 1933 to Doncaster, and he went to Doncaster Grammar School, then in 1937, to March Grammar School (now Neale-Wade Academy); he left school aged 15 in 1939. He became a pharmacist, on a three-year apprenticeship, at a Boots chemist in March, Cambridgeshire. From this he gained an interest in science, and Boots paid for him to do a B.Pharm degree at University College, Nottingham, which he was awarded in 1945.
He rejoined the Boots company in 1945 and worked on their project to produce penicillin. He was moved to the research department of Boots and he went on to research rheumatoid arthritis. This was followed by a PhD in pharmacology at Leeds University returning to Boots in 1952. It was funded by a £300 research scholarship from the Pharmaceutical Society that was matched by Boots and focussed on the heparin-histamine relationships. At the time, the main medicine for the condition were corticosteroids, which had side effects.
At the Boots Pure Drug Company in 1953, Adams began work on other chemical substances that could have a pain-killing effect, and have less side effects, centred on rheumatoid arthritis. He worked in a house in the south of Nottingham for many years, as the main labs had been destroyed in the war, then moved to Boots Pharmaceuticals new building on Pennyfoot Street in 1960 where there was a radioactive lab. This is now BioCity Nottingham.
In August 1958 on Rutland Road in West Bridgford, the team, with Manchester Grammar School-educated organic chemist John Nicholson (1925-83), looked at on phenoxy acids. In 1961 the team started looking at phenyl-propanoic acids, and things were looking good. One of the types was 2-(4-isobutylphenyl) propanoic acid; ibuprofen was first made in December 1961.
Four substances that went to clinical trial failed, and the last - ibuprofen - worked; it was first called RD 13621, and RB 1472. He took the first dose himself and used the drug to treat his own headaches before it was on the market. Animal tests were very encouraging, and tests on humans showed it was about three times stronger than aspirin. He had read in a German journal about ultra-violet-induced erythema on the skin of shaved guinea pigs discovered by Parke-Davis, so he could test anti-inflammatory treatments; the UV-light came from a Hanovia Kromayer Lamp. Some drugs had had amazing effects on albino guinea pigs, but none on humans. It had low GI toxicity in dogs. Boots also now wanted the new chemical to reduce fever (an antipyretic effect). The work was supported in the 1950s by the Empire Rheumatism Council (now Arthritis Research UK). The first clinical trials were by Dr Tom Chalmers at the Rheumatic Diseases Unit at the Northern General Hospital, Edinburgh (which closed around 1990) in 1966.
A patent was filed in 1962, and granted in 1962, for phenylalkane derivatives. In 1969 ibuprofen was licensed as a prescription drug in the UK, and in 1974 in the USA. It was launched in the USA in 1974 by Upjohn of Kalamazoo, Michigan as Motrin. In April 1966, Ibufenac (iso-butyl-phenyl-acetic-acid, known as Dytransin) went onto the UK market, but was withdrawn in January 1968 due to causing jaundice, from its toxicity in the liver. In 1970, Courtaulds Engineering built a £600,000 plant at Boots to make ibuprofen.
In August 1978, Boots applied to have ibuprofen put in general pharmacies, but the Committee on Safety of Medicines (DHSS) declined; in April 1982, there was another request by Boots. Ibuprofen became on sale for general pharmacy (over-the-counter) in 1983, as Nurofen. Adams said in 2007 "Getting the drug approved by the two countries with the toughest regulatory authorities – the UK and the US – was a goal I wanted to achieve. For me, that was the most exciting time of all."
Nurofen was launched 8 August 1983 by Crookes Products Ltd. Ibuprofen went over the counter in the USA in June 1984 by the Food and Drug Administration, made by American Home Products. In America, it was made by Whitehall Laboratories, known as Advil, and also sold as Nuprin. By the late 1980s, ibuprofen was selling around £1.5bn in the USA; in terms of tonnes of production, it was the world's third-most popular medicine. Boots was making about 3,000 tonnes a year. Another big-seller for Boots was Synthroid (levothyroxine, a thyroid hormone). Boots had also developed Manoplax (flosequinan) at great cost (£100m), and it lead to closure of the pharmaceutical division in 1994.
He retired as Head of Pharmacological Sciences at Boots in 1983. For ibuprofen, Boots received the Queen's Award for Technological Achievement in 1985. Naturally occurring oleocanthal was also found by the Monell Chemical Senses Center in 2005 to have a similar effect.
He married his wife, Mary, who was a teacher, in 1950, just before he moved to Leeds where he was introduced to Rugby League. He lives in Redhill, Nottinghamshire in the house he moved into in 1955. in the north of Nottingham. He has become a Freeman of the City of Nottingham. In the 1987 New Year Honours, Adams became an Officer of the Order of the British Empire.