Ahmad Zeidan, of Reading, was sentenced to nine years in 2014 but claims he was tortured into admitting drugs charges.
Zeidan's father said his son was "still rotting in prison" despite the Foreign Office pledging to help last year.
The Foreign Office said it "continued to assist" Zeidan and regularly raises the case with UAE authorities.
UAE authorities previously denied any claims Zeidan has been tortured.
But, Monal Zeidan said his 23-year-old son was a "shattered boy" and was "suffering seizures", three years into his jail term in the emirate of Sharjah, near Dubai.
In 2013 Zeidan, a student at the Emirates Aviation College in Dubai, was part of a group who had accepted a ride in a friend's car when police stopped them and found 0.04 grams of cocaine in the vehicle.
He was accused of possessing and trading in narcotics, but has said the drugs were not his. He claims he was hooded and kept in solitary confinement for two days, stripped naked, threatened with rape and brutally beaten.
The other young men were given pardons or were acquitted but Zeidan, the only British citizen, was jailed.
Monal Zeidan told the BBC: "He was a young student of 19 when he was detained in the UAE three years ago and singled out for the harshest prison sentence of nine years.
"He was a victim of circumstance and simply in the wrong place at the wrong time. His incarceration is a painful tragedy that his family live with every day."
A bilateral meeting took place in March 2016 after Zeidan's case was raised in parliament by Reading West MP Alok Sharma.
But in an email seen by the BBC, a Foreign Office caseworker told his father that during the meeting "it was decided that Ahmad's case did not reach the threshold for Her Majesty's Government to support a clemency request".
This suggests the Foreign Office has made no formal request for a pardon.
On its website it states it would only consider pleas for clemency in "exceptional" circumstances, such as "where a prisoner or close family member is chronically ill or dying" or in cases where it has "evidence that seems to point to a miscarriage of justice".
Human rights charity Reprieve, which had supported the case in the past but now only deals with death row cases, previously said Zeidan's "brutal torture" and the use of "a bogus confession" were "more than enough reason for the British government to request his release".
A Foreign Office spokeswoman said: "We continue to assist a British man who was arrested in the UAE in December 2013.
"Then minister for the Middle East Tobias Ellwood raised the case with his opposite number in 2016 and we continue to regularly raise this case with the UAE government.
"We cannot interfere in another country's judicial system just as we would not allow another country to interfere in ours."
Mr Zeidan said the help has so far amounted to a monthly visit to his son from a British embassy representative.
The family of a British student jailed in the United Arab Emirates over a cocaine find worth about £3 says he has been "forgotten" by the Foreign Office.