Police say they were called to the attraction just after 12.30pm today to reports that a man was wedged underneath a double-decker.
A source said the man had been called to carry out repairs on the vehicle, which had taken a school group to the venue.
They said the jack gave way while he was examining it and he suffered crush injuries.
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Paramedics attended the zoo’s coach park but the man was pronounced dead shortly afterwards.
A Cheshire Police spokesman confirmed the man was 46 years old and from Wigan.
She said: “An investigation into the circumstances surrounding the incident is currently under way and the Health And Safety Executive has been informed.”
The emergency services erected a screen around the bus as a result of the incident. The man’s next of kin have been informed.
Tonight, tributes were paid online to Mr Lannon, 46, from Beech Hill.
Ryan Liptrot wrote on Facebook: “Rest in Peace Wayne a status I never thought I would be writing, a great gent a guy that was class with everyone and it was a pleasure to call you my friend.”
Sharon Jones said: “RIP Wayne. You were one in a million and we will never forget you.”
The bus is understood to have been empty at the time.
The zoo’s chief executive Mark Pilgrim spoke of his “real sadness” following the tragedy.
He said first aid teams and zoo staff helped the emergency services and he expressed his sympathies to the man’s family.