Chesshyre became a Freeman of the City of London in 1975. He was elected a fellow of the Society of Antiquaries of London in 1977 and was a member of its heraldry committee, known as the Croft Lyons Committee. Since 1983 he has been a member of the Cocked Hat Club, the senior dining club of the Society of Antiquaries, serving as "praeses" (president) in 1986. Chesshyre was also a member of the Council of the Heraldry Society from 1973 until 1985, and he was elected a fellow of the Society in 1990. He was vice-president of the Institute of Heraldic and Genealogical Studies (IHGS) and was a Director of the IHGS until 31 December 1993. However, after his sexual offences and the forfeiture of his main honour came to light, "The Observer" reported that the "trustees promptly removed him as vice-president". Chesshyre has been honoured with the titles of associate member of the Society of Heraldic Arts and honorary member of the White Lion Society. He was also the patron of the now defunct Middlesex Heraldry Society.