Prisoners inside HMP Wandsworth are said to be "suffering in sub-zero temperatures" after the heating failed.
The Ministry of Justice (MoJ) said engineers were working to fix the problem - which it claimed was down to UK Power Networks.
Prisoners are said to have been "immediately provided with additional resources for comfort purposes," according to a MoJ spokesman.
However, UK Power Networks said it was not aware of any problems.
The mother of a remand prisoner awaiting sentence told the BBC her son was experiencing "sub-zero temperatures" and it "feels like he is sleeping in a shed".
The MoJ spokesman said: "Engineers are working to resolve a short-term issue with the heating at HMP Wandsworth.
"A generator is in use to provide alternative power. There is no wider disruption to the prison."
Opened in 1851, HMP Wandsworth is a Category B prison and can hold 1,628 inmates.
Temperatures in south-west London have been around -1C (30F) with a "feels like" temperature of -6C, according to BBC Weather.