He had an elder sister, Agatha, and brother, Reynolds, known as Rennie. His mother died on 22 December 1907; in December 1909 his father married Helene Elsie Marion Walker and they had a daughter, Margaret Theodora. His father, mother, and stepmother were all members of the Church Missionary Society; his father was himself born in India of missionary parents. Like Sir Nevill Mott, who was his maternal first cousin, John Simmons was the great-grandson of the Arctic explorer and naturalist Sir John Richardson, after whom he was named.
Simmons was sent home to England to a private preparatory school, entering Windlesham House in Sussex in 1910. In 1916 he obtained a scholarship to Brighton College, as had his brother previously, where he captained the second eleven at cricket. In 1920 he went up to St John's College, Cambridge, to read mathematics, supported by a Bell scholarship. He graduated as a wrangler (first class honours) in 1923. On graduation Simmons immediately accepted the post of statistician and management trainee at J. Lyons & Co. He remained with Lyons for forty-five years, rising to the position of director and chief comptroller, in which post he was head of administration for the company. During that time he pioneered scientific methods of office management, and his drive for efficiency led to the development of the first computer in the world to run a program for business rather than scientific use.
J. Lyons & Co. was best known for its chain of 250 high street teashops and its flagship London restaurants, the Lyons Corner Houses. Managing the paperwork for the hundreds of thousands of small transactions on which the company depended required an administrative establishment of several hundred clerks. Simmons's task was to increase the efficiency of the company's office procedures. Within a few years he had introduced to Lyons the concept of scientific management, based on the principle that there was 'one best way' of doing any task, and that offices should be designed and managed accordingly. To find the 'one best way', Simmons established a systems research office at Lyons (later called the organization and methods department), and some of his lieutenants published books on office management that were influential well beyond Lyons.
In 1925 Simmons became engaged to Muriel Hare (d. c.1992), the daughter of Herbert Sydney Hare, a jeweller from Devon; she had come to London to study Margaret Morris movement, the dance and exercise system named after its founder. They were married by Simmons's father on 10 June 1926 at St George's, Wilton, Somerset. Simmons adored his wife, whom he nicknamed Ariel; there were no children.
A national organization, the Office Management Association (from 1934 the Institute of Administrative Management), had been founded after the First World War. Simmons joined it in 1933, was on its governing council a year later, and in 1938 became its chairman, a post he held until 1950. He was simultaneously its president from 1944 until 1950, and held the title of honorary vice-president until his death. Through this organization he was in regular touch with other influential management figures such as Sir James Pitman. He was an early advocate of decimalization. Among his achievements at the Office Management Association was the introduction of a job grading scheme for office workers based on the system he had introduced at Lyons, which in turn led to the publication from 1942 of a biennial survey, the Clerical Salaries Analysis.
Soon after the Second World War Simmons sent two of his staff, Oliver Standingford and Raymond Thompson, on a lengthy visit to the USA to study developments in office practice. At their request, the visit included meetings with those who had been involved in the development of ENIAC, the so-called 'electronic brain' based on almost 18,000 thermionic valves that had been developed by the US army during the war to calculate firing tables for heavy artillery. By the time they returned, Thompson and Standingford had sketched out a realistic proposal for the development and use of an electronic calculator for routine office work such as invoicing, payroll, and form letters. They had also discovered that Maurice Wilkes at Cambridge University was already building such a machine: EDSAC, the electronic delay storage automatic calculator.
Simmons enthusiastically endorsed their report-he had long dreamed of mechanizing the drudgery of much clerical work. On his recommendation Lyons invested 3000 in EDSAC in return for the right to build its own copy of the machine if it worked. EDSAC, a 3000-valve machine, ran its first programs in 1949. By that time Lyons had already recruited a team of engineers led by John Pinkerton to build its computer, and had created a cadre of systems designers and programmers under David Caminer, then manager of systems research, to develop the first office applications. Simmons himself came up with the name: Lyons Electronic Office, or LEO. LEO I ran its first program, known as bakery valuations, in November 1951, becoming the first electronic computer in the world to run a routine office job. LEO subsequently took on many other jobs, including the Lyons payroll and teashops distribution. The latter, an innovative suite of programs that greatly streamlined the ordering and delivery of goods for the teashops, began to come into use in November 1954.
By this time Lyons was also selling time on the computer to other organizations, from the Ford Motor Company to the Ministry of Defence.
Simmons urged the company to spread the computer development costs by making additional units for sale, and Leo Computers Ltd was founded in 1954. The company built eleven of its improved (but still valve-based) LEO II models, before introducing the highly advanced LEO III, with transistor electronics, in 1962. But the level of investment was never sufficient to compete with American manufacturers, particularly IBM. Despite the successful sales of around 60 LEO IIIs, Lyons sold Leo Computers Ltd to English Electric in 1964.
For Simmons the computer was always a means to an end, not an end in itself.
In 1962 he published LEO and the Managers, which set out his vision of the computer as a management tool at the heart of a business. In it he wrote:
LEO is to the thinking of a manager as a grammar book is to the words of a speaker ... The use of LEO brings a new freedom and power to managerial thinking and decision making and ... a means of unambiguous communication.
He had drawn up a 'master plan' for Lyons, neatly encapsulated in a flow chart that showed how information would stream between autonomous divisions and the board via the computer. But it was never fully implemented: Simmons never succeeded in persuading board members to make full use of LEO's powers of analysis. By the time he retired from Lyons in 1968, minicomputers were becoming available and divisional managers were acquiring their own. After retirement he wrote The Management of Change (1970).
While unfailingly courteous, Simmons was perceived by his juniors as austere and exacting, demanding precision in speech and writing and a clear sense of purpose. He dressed formally in double-breasted suits until his retirement, after which he rather surprisingly grew a beard and favoured bow ties and velvet jackets. Throughout their marriage he and Muriel moved between addresses in west London, finally settling in Hyde Park Gardens. Between 1965 and 1974 they also owned a flat in Ospedaletti on the Italian riviera.
Simmons was not a regular churchgoer but retained a deep personal belief. He died in St Mary's Hospital, Praed Street, London on 14 January 1985, following a stroke, and was cremated at Mortlake. His wife survived him for a further seven years. Since 1968 an annual lecture has been given in his honour under the auspices of the Institute of Administrative Management.