Abu Dhabi, United Arab Emirates (CNN) -- Britain says it will continue to press for an independent investigation into the case of three British citizens who say they were tortured before being sentenced Monday to four years in prison on drug charges in the United Arab Emirates.
Grant Cameron, Karl Williams and Suneet Jeerh, all in their mid-20s, say they have been subjected to electrical shocks and other abuse.
In a letter to London-based legal charity Reprieve, British Prime Minister David Cameron wrote that "our concerns about the allegations of torture ... have been repeatedly raised with the Emirati authorities, including by the Foreign Secretary and (Foreign Office Minister) Alastair Burt."
The prime minister added that "the absence of an independent medical examination (of the men) remains a concern," and that Britain continues to press for evidence of a full, impartial and independent investigation.
The manager of the Dubai police human rights department, Mohammad Al-Mur, said investigators looked into allegations that the men had confessed after being tortured and found no evidence to support the claims.
Al-Mur told CNN Arabic that men's accusations "were rejected after being investigated in accordance with international standards by Dubai police."
The developments come a day ahead of UAE President Sheikh Khalifa bin Zayed al Nahyan's scheduled state visit to Britain.
Cameron, Williams and Jeerh were arrested in July and charged with consumption and possession of the synthetic cannabis product known as spice.
Their conviction Monday on the consumption charges carries a minimum of four years of imprisonment.
The supply charges against the men were dropped, said Kate Higham, a lawyer for Reprieve. Higham has been in touch with the defendants' attorneys, who have declined to speak with CNN.
While pleased that the defendants did not get heavier sentences, "we think they should not have been convicted at all," Higham said.
"We will continue to push for the men's release and return in light of the torture they have suffered. We hope the UAE president would take this opportunity to show that he shares the British public's concern about torture," Higham said.
The men could have faced 15 years if convicted of possession with intent to distribute.
In a text, Cameron's mother, Tracy Cameron, called the sentence "great news."
Claims of abuse
The men say police beat them and subjected them to electric shocks after their July 10 arrest, according to Reprieve, which provides legal support to prisoners.
The case began when Cameron and Williams were visiting Dubai on vacation.
Jeerh had moved to Dubai from Britain about six weeks earlier in hopes of getting a job in media, Higham said.
The Britons were driving a rented car, and when they reached Jeerh's apartment building, they were arrested.
The three allege they were then taken to the desert and then to Williams' and Cameron's hotel, said Marc Calcutt, who had earlier represented them on behalf of Reprieve.
"I remember that the police put a towel on my face so I could not see. They kept telling me I was going to die," Williams said in a statement released by Reprieve. "Then they took off the towel and I could see that there was a gun pointed at my head ... I started to believe that I was going to die in that room."
At one point, police pulled his pants down and zapped his testicles with electric shocks, Williams alleged.
Calcutt also said Williams' hand was kicked until it was broken and said he has X-rays to prove it.
Tracy Cameron said her son told her that police used a Taser on him and put guns to their heads, but she said she hasn't been able to get all the details because he is never alone.
The men were pressured to sign documents in Arabic, without translation, after multiple beatings, Reprieve said.
A "neutral party" appointed to investigate if any torture had occurred found the claims untrue, a Dubai police statement released in February said.
But Calcutt said he was skeptical.
"No one knows who that neutral party is. I have not seen a report. I would love to see any investigative report," Calcutt said.
Leone Lakhani reported from Abu Dhabi, and Holly Yan wrote from Atlanta.