Robert Carson, who died on March 24 aged 87, was a leading expert on Roman coins, and Keeper of Coins and Medals at the British Museum from 1978 to 1983.

Born at Kircudbright on April 7 1918, Robert Andrew Glendinning Carson was educated at Kirkcudbright Academy and the University of Glasgow, where he took a First in Classics. During the war he served with the Royal Artillery in north-west Europe, being promoted to captain in 1945.

The following year Carson joined the Department of Coins and Medals at the British Museum as an assistant keeper with responsibility for Roman coins, as the successor to Harold Mattingly. The offices of the department had been destroyed by a bomb in May 1941, and, although the collection had been removed to a place of safety, the work of the staff in the immediate post-war years was to rebuild the department. They did not return to their original premises until 1959.

Carson quickly established his reputation, initially by publishing new hoards and acquisitions. He developed an interest in the coinage of the 3rd century AD, the understanding of which was at that time shrouded by misattributions and misunderstandings. Written evidence of the period is limited, so coinage has seemed to offer the only systematic body of evidence on which even the most basic political and military history could be written.

The "crisis" of the 3rd century may nowadays be downplayed by historians, but it was a period of short-lived and competing emperors, and a time when the coinage saw a dramatic decline in purity, possibly suggesting an economic crisis coinciding with the political ones.

Carson's approach was pragmatic and straightforward: he marshalled the evidence and drew sensible, but not over-ambitious, conclusions. His work can be seen at its best in his sixth volume of the Catalogue of Coins of the Roman Empire. Published in 1962, it set out a systematic and convincing account of the coinages of the years 222-238, and applied his more theoretical studies of the "officina" (workshop) system of the mint of Rome.

He never completed the systematic studies he planned for the more complicated years of the middle and later part of the 3rd century, but finished many preliminary studies, including of the eastern mints of Valerian and Gallienus, of Zenobia (Queen of Palmyra, 267-272), and coinage after the reform of Aurelian, a study informed by the discovery of an enormous hoard of relevant coins at Gloucester in the 1960s.

Carson had a specific interest in the coinage of the British usurpers Carausius and Allectus, who established a separate empire in Britain in the 280s and 290s AD; and he sorted out the pattern of mints and chronology in a way that had not previously been achieved. He became very excited at the appearance of two large bronze medallions of Carausius - which he was delighted to ensure got a safe home at the museum - and was once observed to sign a letter "RAG Carausius".

Carson had a keen interest in conveying his knowledge to interested amateurs. He was a popular lecturer and wrote three general books: Principal Coins of the Romans, published in three volumes between 1978 and 1981; Coins of the Roman Empire (1990); and Coins - Ancient, Medieval and Modern. This last volume, first published in 1962, went through numerous reprintings and revisions over two decades, remaining the best single account of the coinage of the world as a whole.

As well as his own work, Carson was instrumental in ensuring that important works by other scholars also saw the light of day.

As editor of the Roman Imperial Coinage series, he can take much credit for the eventual appearance of three volumes, the first by the late JWE Pearce, the second by the Finnish scholar Patrick Bruun, and the third by his museum colleague John Kent. He and Kent had collaborated on the classification of the bronze coinage of the 4th and 5th centuries AD, and on a short but indispensable reference book, Late Roman Bronze Coinage (1960, written also with Philip Hill).

Carson's work on identifying coin finds occupied much of his time and led to many other publications, including an influential analysis of the pattern of hoarding in late Roman Britain, and to an enormous programme of acquisition for the museum.

The trays of coins of the later Roman empire were built up to provide an indispensable reference collection for modern scholars of the period.

He also became involved in many coroners' court hearings on Treasure Trove, the law whereby hoards of gold and silver are deemed to belong to the Crown. By arguing that "silver" meant "intentionally made of silver", he persuaded many coroners to rule that hoards of very base silver coins, sometimes containing as little as two per cent of silver, were also Treasure Trove.

A tall, elegant man, Carson was quiet and self-effacing but determined in leadership. He devoted much time to administrative matters, and, with his wife Fransisca, was a lively presence at departmental parties.

He performed excellent work as editor of the Numismatic Chronicle of the Royal Numismatic Society, and the volumes for 1966 to 1978, for which he was responsible, take up a vital half-metre of many research libraries. As president of the International Numismatic Commission, he was also influential in the organisation of the International Numismatic Congress of 1986, which was attended by more than 700 experts from all over the world.

After retiring from the museum, Carson emigrated to Australia.

He was elected a Fellow of the Society of Antiquaries in 1965, and President of the Royal Numismatic Society in 1974. He was awarded the medal of the French Numismatic Society in 1970; the Silver Medal of the Royal Numismatic Society in 1972; and the Huntington Medal of the American Numismatic Society in 1978. In 1977 he was awarded a Silver Jubilee Medal by the Queen.

He was elected a Fellow of the British Academy in 1980.

Robert Carson married, in 1949, Fransisca de Vries, who survives him with their son and daughter.