A British schoolboy who was allegedly abducted in Qatar nearly three years ago has appealed to David Cameron to help reunite him with his mother.

Adam Jones was separated from his British mother while visiting his dead father's relatives in the Qatari capital Doha in October 2009. Since then the 13-year-old says he has been kept under virtual house arrest despite attempts by his mother, Rebecca Jones, to free him.

Adam also claims he has been punched and kicked by family relatives. He says he is not allowed out alone, has no internet access and is unable to call his mother. Cameron has written to his Qatari counterpart, Sheikh Hamad bin Jassim bin Jabr al-Thani, and the Arab state's emir to demand that "Adam's voice is heard" and that the case is "speedily resolved".

In a recent letter to Adam, the prime minister pledges that he will personally keep urging the Qatari royal family to ensure that his wish to return to his mother will be granted. Cameron states: "I was very sorry to read that you are still separated from your mum. This must be very hard for you, but I want you to know that you are still in my thoughts. I will keep trying as hard as I can to help you, and I hope your family situation will change for the better very soon."

In a handwritten addendum, Cameron states: "I promise I have not forgotten about you – and will keep trying to make some progress."

His letter followed a plea from Adam, who 11 months earlier had turned to him in desperation. Dated 25 April 2012, Adam states: "It is nearly one year since I wrote to you asking for your help. I was so happy when you wrote back and told me you would do your best to help me get home. Did you forget about me?

"I want to go home now and I'm very sad and lonely."

Adam reveals that he has also asked for Prince Charles's intervention because "nothing has happened and I think no one cares about me".

The alleged abduction of Adam is a continuing focus of diplomacy between Britain and the Arab state, his case having being raised personally by the Queen during a meeting with Thani. The Foreign Office's child abduction section is also involved, with a spokesman saying it recognised the "enormous distress faced by Rebecca Jones in being separated from her son and we sincerely hope she is reunited with him soon".

Yet Thani's written response to Cameron states only that he will try "to find an amicable solution that preserves the rights of all parties involved".

Jones said her son was effectively a prisoner at the high-walled, gated home of his Qatari relatives and was forbidden to visit friends. Even at school, the 45-year-old from Sheffield claimed, Adam was escorted between classrooms and held in a room after lessons to be picked up by relatives.

The ordeal began after she and Adam were invited to visit the parents of her late ex-husband on 3 October 2009. Rebecca was separated from Adam's Qatari father Jamal, who died in a motorbike accident in 2005, but stayed in contact with his family to allow them access to Adam.

On the morning they were due to return to Bahrain, where Jones had taken a teaching job, she said she received a call asking if Adam could visit his sick grandmother. She agreed and a driver picked up Adam. Shortly after, his uncle, Fahad al-Mudhaki, rang and asked to meet her to discuss dividing up the proceeds of land belonging to Adam's father. Although the documents were in Arabic, Jones says she trusted Mudhaki's explanation that they comprised paperwork designed to safeguard Adam's inheritance and signed them. "I just wanted to go home with my son and was not interested in the lands or money my son had been left by his father. It did not occur to me what would happen."

The documents were to be used to kickstart the Mudhakis' custody claim against her. Within minutes of signing, Jones says she realised she had been duped. She alleges that her husband's relatives told her that she had been deliberately deceived: "I'll never forget what Adam's uncle Fahad told me: 'I have lied to you and tricked you, Jamal did not take your son but I will'."

The Mudhakis had made a court order in 2008 to win custody of Adam, confirming to her the abduction was premeditated. A custody hearing was already arranged for 13 October, days after the alleged kidnapping. "I felt sick to the stomach to realise that I had fallen easily into their trap."

Adam, then 10, has been separated from his mother ever since, despite a series of custody appeals and Jones's offer to waive Adam's inheritance. A subsequent hearing ruled that Jones, who also has a four-year-old daughter Alex, is allowed to visit Adam twice weekly, but never unsupervised.

She says the teenager is increasingly depressed. Since being taken, Adam has seen his sister twice, while the Mudhakis refuse to let Adam's British grandmother, 74, visit him.

"For the last three years Alex won't sleep in her own bed," said Jones, "she's scared somebody is going to take her."

Fahad Mudhaki is a senior police officer, a fact which Rebecca believes he has used against her. During her first visit to see Adam, eight weeks after he was taken, she said that 15 armed police officers surrounded the Mudhaki house and Jones was flanked by officers throughout their meeting. She says she has suffered a constant campaign of intimidation, sometimes receiving up to 20 calls a day from police, and each time she enters Qatar to visit Adam is terrified that she might be arrested.

A document from the British embassy in Doha states "the child was kidnapped by his uncle Mr Fahad Juma Abdullah al-Mudhaki, a Qatari police officer".

Jones said: "I've been terrorised and treated as a criminal. We are still suffering every day without our little boy. The pain has not gotten easier as time has passed because I cannot accept what has happened."