Linda De Sousa Abreu, 30, of Fulham, was charged after the video began to circulate on social media.
A police investigation was then launched and De Sousa Abreu was arrested and pleaded guilty to misconduct in public office, at Isleworth Crown Court, in July last year.
She appeared at the same court on Monday (January 6), where she was sentenced to 15 months in prison.
The charge says that De Sousa Abreu “wilfully and without reasonable excuse or justification misconducted yourself in a way which amounted to an abuse of the public’s trust in the office holder by engaging in a sexual act with a prisoner in a prison cell”.
It happened at Wandsworth between June 26 and 28.
She was arrested at Heathrow Airport and was due to catch a flight to Madrid, having notified the prison of her travel plans.