Machin was born in Stoke-on-Trent in 1911. He started work at the age of 14 as an apprentice china painter at the Minton Pottery. During the Depression he learnt to sculpt at Stoke-on-Trent's Art School, which was opposite the Minton factory. In the 1930s he moved to Derby, where he worked at Royal Crown Derby and met his wife Patricia. He went on to study at the Royal College of Art in London.
After imprisonment in the Second World War as a conscientious objector, he returned to modelling and sculpture, and created many notable ceramics which are now prized collectors' items. In 1947 he was elected an associate member of the Royal Academy, was appointed a Master of Sculpture from 1959 to 1966 and became the longest-serving member of the Academy. He was elected an Academician in 1956 and a Fellow of the Royal Society of British Sculptors. From 1951 he was a tutor at the Royal College of Art.
In 1964 Machin was chosen to design a new effigy of the Queen for the decimal coinage, which was to be introduced from 1968. This effigy was used for all British coins until 1984. It was first used on the Half Crown coin of Rhodesia in 1964, coins of Canada from 1965 to 1989, Australia from 1966 to 1984 and New Zealand from 1967 to 1985.
In 1966 the Queen approved Machin's similar design for an effigy of her to be used on what came to be known as the "Machin series" of British definitive postage stamps. Machin produced a bas-relief in clay which, when combined with a different coloured background, is reminiscent of the overlaid decoration of potteries such as Wedgwood. The design was first used on the 4d value which was issued in June 1967, and has been used on all British definitive stamps (except more recent regional issues) ever since. It is thought that this design is the most reproduced work of art in history with, to date, approximately 320 billion copies produced.
On several occasions the Queen has been approached with suggestions for the replacement of the Machin stamp portrait. Although she has considered alternatives, she has never approved any new design, stipulating that any such replacement would have to be "a work of real quality".
In 2007 the Machin-designed stamp was still in use at its 40th anniversary and to mark the occasion, the Post Office issued a commemorative stamp featuring a photograph of Arnold Machin. It was also available for sale in a miniature sheet which incorporated another stamp with a reproduction of a Machin series stamp as well as two £1 Machins in different colours.
In the 1956, while resident at number 15, The Villas, Stokeville, (an estate of 24 Victorian houses in Stoke-upon-Trent) he received publicity in the national press when he chained himself to an old metal lamp-post in protest at its planned removal. Machin's protest, "against the destruction of all the beautiful things which is going on in this country" did not prevent the lamp-post from being replaced by a concrete one; however, it was given to him for his own garden and his wife Patricia unlocked him. The lamp has since been restored to its original position.
Machin and his wife Patricia had a son, Francis (1949-2007) who was also an artist, and an architect. After Francis died, the possessions of Arnold Machin in his house near Eccleshall in rural Staffordshire were sold in auction. The possessions included the fourth of the final plasters known made to create the Machin stamp series, the three others are kept in the Royal Mail archives.