Ahmad Zeidan, 23, was sentenced to nine years in 2014, but claims he was tortured into admitting drugs charges.
His father Manal Zeidan said that his son, from Reading, decided to stop his hunger strike after being visited by a British official in prison.
The Foreign Office said it was continuing to assist Zeidan.
UAE authorities have previously denied all torture claims against Zeidan, who is being held at a prison in Sharjah.
Zeidan was a student at the Emirates Aviation College in Dubai when police found 0.04 grams of cocaine, worth around Â£3, in a friend's car he was a passenger in.
The other men were given pardons or acquitted but Zeidan, the only Briton in the group, was jailed for nine years.
Mr Zeidan said his son had not eaten for a "few days" but was persuaded to end his stance after meeting with a representative from the British embassy.
He said he had been promised the UK would raise the case again formally if a motion to reduce his sentence at a court hearing next month was successful.
"If the motion fails or the Foreign Office does not formally raise his case then he will restart his hunger strike," Mr Zeidan added.
"I am very worried about his health and his hopelessness.
"He told me he can't take much more of this."
A Foreign Office spokeswoman said the case was "regularly" raised 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," she added.
A British student in a United Arab Emirates jail has temporarily ended a hunger strike over the UK government's "lack of action".