The blaze broke out early morning in the Patas monkeys' house within the jungle drive-through enclosure at Woburn Safari Park, located in Milton Keynes town, the Independent reported.
A spokesman for the park said: "Staff and fire crews attended the scene; however, devastatingly for everyone at the park, none of the 13 animals could be saved."
No other animals were harmed, the spokesperson said. An investigation was under way into the cause of the fire.
The 1.5 square km safari park, opened in 1970 and housing various wildlife including elephants, zebras and lions, is part of the estate of the Duke of Bedford, which also features Woburn Abbey, one of Britain's best-known royal homes.
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