A prosperous draper and tailor in Newport, Frost served as a member of Newport's first elected town council (from 1835), as magistrate (1836–39), and as mayor (1836–37). He was a delegate from Monmouthshire to the Chartist convention in London (February–September 1839) and occasionally was convention chairman, in which capacity his tie-breaking vote dissolved the assembly. Returning to Newport, he became involved in militant Chartist activities that culminated in the street battle on November 4.

Convicted (January 16, 1840) of high treason, Frost received a death sentence, which was commuted to exile for life to Van Diemen's Land (now Tasmania). Released in 1854 on condition that he leave British territory, he lived in the United States until 1856, when he was granted a full pardon. Frost became an advocate of prison reform, including the end of convict transportation, and he wrote newspaper articles and lectured in England.