The son of a successful medallist, also called Allan, he was born in London and educated at Highgate School. He studied at South Kensington under Sir Hamo Thorneycroft, where he won silver medals. His first RA exhibit was a medal depicting his father. Having decided on ordination in the Anglican church, Wyon moved to Saltash in 1935, and was then appointed Vicar of Newlyn.

He was married to the painter Eileen WYON (nee Le Poer Trench).

He first became involved with the Newlyn Society of Artists in 1936, exhibiting a large sculpture, The Sorrows and Mankind, in the NAG Exhibition of 1937, and remaining a staunch supporter until he left the district in 1955. Wyon opened the STISA Summer Exhibition of 1943, and it may have been this occasion that prompted him to become involved with STISA, the first distinguished sculptor to do so (Tovey).

To demonstrate the close links between the Newlyn and St Ives Societies, the Committee of the Newlyn Society in 1943 comprised Wyon, Dod PROCTER, Eleanor HUGHES and Alethea GARSTIN, all of whom were members of STISA. Unsurprisingly his sculptures often had a religious subject, and one of his finer pieces was The Worshipper. On the death of Stanhope FORBES in 1947, Wyon was commissioned to produce a sculptured panel of Forbes' head, and this was fixed to the lower front façade of the Newlyn Art Gallery, unveiled in 1948 by Sir Alfred MUNNINGS, then both President of the RA and STISA.

 Also in 1947, the final year of the life of Robert Borlase SMART, he painted a portrait of that prominent painter-artist (Whybrow). A highly-rated medalist, he was responsible for artistic work at the Royal Mint, and also exhibited some medal works with STISA.

A correspondent (2018) has sent us a link to a British Pathe news clip of 1941, showing the Rev Allan Wyon in his studio, creating the wax model for the Lloyds War Medal for Bravery at Sea, later cast in silver. 

A correspondent (2023) has told us of a portrait which he purchased, painted by and signed 'E M Wyon' (Allan's wife Eileen). It is possible that the sitter may well have been Allan Wyon. Although it was listed at auction as 'a portrait of an unknown gentleman', a note on the back of the frame by a previous owner suggests that this was indeed a portrait of Allan Wyon.