In 1843, Bunning was appointed Clerk of the City's Works to the
City of London in 1843, a post for which
William Tite had also been a candidate. In this role he built the Coal Exchange in
Thames Street (1849); the
City Prison at Holloway, Billingsgate Market (1853), in red brick and stone, in an
Italianate style, with a central campanile; the Freemens' Orphans' Schools in
Brixton, also Italianate and in red brick and stone (1852–54), and the
Metropolitan Cattle Market in Islington, opened in 1855. He had previously made a design for remodeling the market on its existing site at Smithfield. The central
clock tower, in what is now Caledonian Park, and two sets of railings are all that remain following the market’s closure and demolition in the early 1960s. In 1856, he built two law courts at the Guildhall, and in 1858 began the complete reconstruction of
Newgate prison, leaving only
George Dance's outer walls intact. In 1858 he built Rogers' almshouses at Brixton and the
Pauper Lunatic Asylum at Stone in Kent, both in a "domestic Gothic" style. He also surveyed and planned many road improvements, including the building of New Cannon Street (opened in 1854). His unexecuted projects included one for the widening of
London Bridge. ==Family==