Grant Cameron and Suneet Jeerh, both 25, and Karl Williams, 26, were arrested while on holiday in July last year after police claimed to have found drugs in their car.
On Sunday, the Prime Minister called for a full investigation into the allegations and vowed to raise the issue during a state visit by the president of the United Arab Emirates (UAE) to the UK on Tuesday.
The three men, who are from London and Essex, were arrested on 10 July 2012 after police claimed to have found a synthetic cannabis known a 'spice' in the car they were driving.
According to accounts by the men provided to Reprieve, they were driven to a location in the desert where they were tortured.
They kept telling me I was going to die. I was so scared. Once I had been knocked to the ground, the police picked me up and put me on the bed. They pulled down my trousers, spread my legs and started to electrocute my testicles. It was unbelievably painful. I was so scared.
The torture allegedly also took place at a police station and hotel and all three were made to sign documents written in Arabic - a language they do not understand.
The government of the United Arab Emirates (UAE) has flatly denied the allegations.
In a letter to Reprieve, the Prime Minister has said he will use a state visit by the UAE president, Sheikh Khalifa bin Zayed Al Nahyan, on Tuesday to raise his concerns.
The UK Government takes all allegations of mistreatment very seriously. We continue to press for evidence for a full, impartial and independent investigation into the allegations. The absence of an independent medical examination remains a concern.
Responding to his comments, Reprieve investigator Kate Higham said it was "hard to see" how the president's visit is appropriate given the gravity of the allegations.
Grant Cameron's mother, Tracy, said she was convinced the police in Dubai treated her son and his friends "appallingly".