The former Manx Grand Prix winner sustained ‘extensive injuries’ in the incident and spent the night in intensive care.
His family said he underwent surgery to stabilise him before the transfer flight to Liverpool.
In a statement, his daughter thanked well-wishers for their messages of support and asked people to ‘say a prayer for him’.
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“Will post when we know more,” read the family statement on Facebook.
“Thank you on behalf of the Moffitt/Griffith family for the messages and well wishes. Messages are coming through thick and fast, we have read them and really appreciate the support. Please say a prayer for him.”
Meanwhile, the TT organisers provided an update on the riders who were involved in crashes during Monday’s qualifying session.
Sam West, who came off at Laurel Bank, causing a red flag, has been discharged from Noble’s Hospital.
Irish road racer Michael Sweeney, off at the 11th Milestone, has also been released from hospital, while James Chawke and Jonathan Perry – who crashed at Union Mills and Cruickshanks respectively – have been passed fit again by the TT medical team.
Dutch newcomer Llja Caljouw, off at the 27th Milestone, has also been discharged from hospital.