Cunliffe, who reportedly emigrated from Britain in 1967 and is now in his 60s, today lost an appeal against the Australian Department of Immigration's decision that he should be deported to the UK.
He has been placed in an immigration detention unit while arrangements are made to remove him.
A department spokeswoman said: ''The Federal Court dismissed Mr Cunliffe's appeal against the ministry's decision to cancel his visa so now he continues to be an unlawful non-citizen.
''He remains in immigration detention until arrangements can be made for his deportation.''
Australian Federal Court Justice Julie Dodds-Streeton made the ruling at a hearing in Melbourne.
The department spokeswoman gave no indication of how long it would take to deport Cunliffe, but said arrangements would be made ''as soon as possible.''
A series of ageing British sex offenders have been deported back to the UK under Australia's tough immigration policy.
Paedophile Raymond Horne was removed to Britain in March 2008 having served a 12-year prison sentence for 14 sex offences.
He lured two homeless boys, aged 13 and 15, to his flat while volunteering for a charity.
Horne had moved to Queensland from Britain in 1952, but never became an Australian citizen and on his release the authorities revoked his visa.
In July 2005 Robert Excell was deported to Britain after spending 37 years in Australian prisons for child sex convictions dating back to 1965, when he raped a seven-year-old boy.
Excell was born in the UK and emigrated to Australia when he was 10, but never took citizenship.
Convicted murderer and serial rapist Simon Wilson, who had lived in Australia since he was two, was sent back to Britain in January 2008 after being released on licence from a life sentence for killing an elderly woman with up to 100 punches.
Three months later he attacked and tried to rape a frail 71-year-old woman in Camden, north London.