The artist is unknown for this miniature portrait.
However the sitter is identified via a scratched inscription made by an amateur hand around the rear of the frame. It appears to read; "James Bedolfe - 1872 OB - 1829 born at Ovingdean".
Bedolfe seems to be a spelling variant of Biddulph and Ovingdean is a reference to the Ovingdean, a small village two miles east of Brighton, which is now part of Brighton, see Ovingdean - Wikipedia, the free encyclopedia
Bedolfe is a very uncommon name and in trying to find likely relatives in that area of England, one possibility who may be a son, is recorded in the 1881 census for Portsea Island Borough Lunatic Asylum, Portsea, Hampshire, England.
There in 1881 was a resident, apparently an inmate, named as "Paton Davenport Bedolfe" aged 26, formerly a medical student. His age would fit with being a son of James Bedolfe. The name may even be meant to be "patient Davenport Bedolfe". Portsea is about 40 miles far from Brighton.
There are several men named James Biddulph, including a bricklayer in Staffordshire with the same birth and death dates, who is in all the relevant census records, but he seems to have lived and died in Staffordshire. Without the reference to Ovingdean, it would seem that this is the most likely person to be the sitter in the miniature.
Alternatively, it may be that he is recorded under another spelling variant. 72