Three British men who say they were tortured in Dubai before being found guilty of possessing drugs have been pardoned under a Ramadan amnesty three months into their four-year prison sentences.

Grant Cameron, Suneet Jeerh and Karl Williams were jailed in April for possessing a quantity of synthetic cannabis known as spice.

They said they were given electric shocks and had guns held to their heads during a seven-month period when they were held without trial.

The London men were pardoned a year after they were arrested when drugs were found in their car while on holiday in the United Arab Emirates. They denied charges of "consumption and possession with intent to distribute".

Cameron is now back in London, while Jeerh and Williams are awaiting deportation from Dubai.

In a statement issued through the human rights charity Reprieve, which has been campaigning for the men's release, Cameron's mother, Tracy, said: "After a year of waiting, we are deeply relieved and overjoyed to have Grant back home with us after his terrible ordeal. We hope that his friends Karl and Suneet will soon also be safely back in Britain.

"Obviously what Grant has been through has been very distressing for him, and the family as a whole. We'd ask that people give him the time, space and privacy he needs to settle back in."

In April Tracy Cameron said her son and his friends had been Tasered and beaten. In Williams' witness statement he said his testicles had been electrocuted during interrogation by the police. The men's lawyers said they were forced at gunpoint to sign documents in Arabic, which none of them understands. The Emirati police deny the allegations.

The Jeerh family was reluctant to discuss Suneet's case until he had safely returned to the UK.

His brother Aneet said: "It's all up in the air. He's in better spirits than he was three weeks ago, when there was a big black cloud hanging over them and they didn't know which way the events were going to turn.

"We always knew that they [the Emirates authorities] were not going to admit that they made a mistake. But sending them home is their way of squashing the other issues that have come out of this case."

Reprieve investigator Kate Higham said: "After everything Grant has been through, his release is welcome but long overdue. No one should have to go through what he experienced, and we are glad that he is safely back home."

The men's allegations of torture were raised by the prime minister, David Cameron, during a state visit in April by the UAE president, Sheikh Khalifa bin Zayed Al Nahyan. This week the sheikh freed the men under an amnesty timed to coincide with the Islamic holy month of Ramadan.

A spokeswoman for the Foreign Office said she could not discuss individual cases, but added: "We are aware that the 2013 amnesty list has been announced in the United Arab Emirates and that the local authorities have begun the process of releasing those included. This will continue to come as welcome news for those included and their families. We will continue to provide appropriate consular assistance."

Figures released by the Foreign Office showed that many Britons had fallen foul of the UAE's tough drug laws. The British embassy in Dubai helped 257 Britons who were arrested or detained on drugs charges in the last year. This represented almost half the embassy's caseload.

The Foreign Office travel advice for the UAE warns Briton's that the Emirati authorities regard even the presence of drugs in the bloodstream as possession.

It says: "The penalties for drug trafficking, smuggling and possession, of even residual amounts, of drugs are severe. Sentences for drug trafficking can include the death penalty and possession of even the smallest amount of illegal drugs can lead to a minimum four-year jail sentence … you should take care over the import of prescription drugs, some over-the-counter drugs and certain substances known as herbal highs, such as Spice or Space, which can include synthetic cannabinoids.