The survival rate of prison records is very patchy. Under the Public Records Acts 1958 and 1967 the Home Office has a duty to preserve its records of historical and public interest, including those of prisons, but this understanding of the importance of prison records was a little late in the day to save many records particularly of prisons that had closed. The earlier they closed the less likely any records would survive.
Newgate prison closed in 1902. The prison registers are held by The National Archives.
Horsemonger Lane Gaol Newington Southwark 1799-1878 was Surrey’s principle prison replacing the old county gaol and House of Correction in Southwark. It housed debtors as well as criminals and was Surrey’s place of execution for criminals. Besides Horsemonger Lane Goal opened in 1851 was the Surrey House of Correction in Wandsworth. When Horsemonger Lane Gaol closed in 1878, its execution duties were transferred to Wandsworth. Wandsworth prison is now the largest prison in London and one of the largest in Western Europe. The registers for Wandsworth prison survive and are held by the London Metropolitan Archives.
In 1889 the metropolitan areas of Surrey such as Southwark and Wandsworth became part of London.
Basically there is nothing that really survives for Horsemonger Gaol and that is borne out by the fact that the three record offices which might hold the records for gaols in the London area have all have come up with nothing. This will be the case for other goals - compters, lockups, bridewells and Houses of Correction/Detention in London particularly when they closed before the start of the C20th.
What you can research however is his records at Bethlem Hospital. The hospital maintains its own archives.http://www.bethlemheritage.org.uk/