"He has stated that he would become suicidal and he told me that he would 'drink himself to death'," said Dr Slater.
"Overall, I believe that there would be a significant risk of Mr Sheridan suffering psychiatric harm if he was forced to accept the accommodation proposed by the council.
"I do not think it would be overstating it to say that it could amount to a death sentence for him."
But appeal judges Sir Andrew Morritt, the Chancellor of the High Court, Lord Justice Patten and Lord Justice Pitchford ruled in the council's favour and dismissed Mr Sheridan's appeal.
Lord Justice Patten said in a written ruling - handed down today after a hearing in London in February - that the council had not been "unreasonable", interfered with Mr Sheridan's human rights or made any "error of law".
Council officials had said no traveller plots were available in Essex - and Lord Justice Patten said there was "really no evidence" to support an argument that "possible sites" existed.
He said a local authority could not be required to acquire land as part of a duty to provide accommodation for homeless people.
The council said local health services could deal with Mr Sheridan's "pyschiatric" problems - and Lord Justice Patten said that approach was "not unreasonable".
Judges dismissed similar appeals by Mr Sheridan's estranged wife, Barbara, who looked after the couple's three children, and traveller Mary Flynn.
They said all three travellers had lived at Dale Farm and were eligible for "housing assistance" because they were "not intentionally homeless" and were in "priority need".