Career
Charleton was educated at the University of Oxford, where he took the degrees of Master of Arts, Bachelor of Medicine, and Doctor of Medicine He settled in practice at Bath, Somerset, was elected physician to the Bath General Hospital 2 June 1757, and then lived in Alfred Street. He belonged to the Royal College of Physicians. Charleton wrote on the chemistry of mineral waters, and was elected Fellow of the Royal Society on 3 November 1747.
He then retired from the Society, in 1754.
He resigned his post at the hospital 1 May 1781, and died in 1789.