Algerian sex offender Brahim Kaddour-Cherif was arrested on Friday after being released on 29 October, while William Smith handed himself back in to the south London prison on Thursday.
Migrant sex offender Hadush Kebatu, who arrived in the UK on a small boat, was mistakenly released from HMP Chelmsford in Essex.
A Ministry of Justice spokesperson told the BBC: “The vast majority of offenders released by mistake are quickly brought back to prison, and we will do everything we can to work with the police to capture the few still in the community.”
Earlier, shadow justice secretary Robert Jenrick said the unaccounted prisoners revealed “the incompetence of this government”.
“It shouldn’t be left to reporters to uncover the facts. [Justice Secretary] David Lammy must finally come clean about how many prisoners have been accidentally released and how many are still at large.”
A spokesperson for the Liberal Democrats said “every resource” must go into finding the prisoners.
“This is a disgrace and an omnishambles. It shouldn’t have to take the media to inform the public that prisoners are at large after accidental release,” Jess Brown-Fuller said.