The UAE president came under pressure from Prime Minister David Cameron on Wednesday over allegations that three British men jailed in Dubai were tortured.
Cameron raised the issue with Sheikh Khalifa bin Zayed al-Nahyan, the United Arab Emirates' head of state, during talks before the end of his two-day state visit to Britain, his Downing Street office said.
The British premier stressed the need for an independent investigation into the allegations of police mistreatment made by the three Britons who were jailed for drug offences.
The three Londoners in their 20s, who were each jailed for four years, were subjected to beatings and electric shocks, campaigners have claimed.
Cameron and Khalifa also discussed Iran's nuclear programme, Syria, the Middle East peace process and Somalia.
They talked about moves "to address the challenge of Iran's nuclear programme, to end the appalling and dangerous conflict in Syria, and to bring new momentum to the peace process between Israel and Palestine."
The pair also spoke about the defence and commercial relationships between Britain and the UAE.
The mother of Grant Cameron, one of the men jailed, welcomed the prime minister's intervention but said: "I would like him to go one step further and see whether he can ask Sheikh Khalifa, if it's appropriate, to expedite any pardons that are going to be given to the boys."
Tracy Cameron said the case had been a "catastrophic" experience for the three men's families, but was "very confident" progress could be made.
Britain's Foreign Secretary William Hague underlined London's unease at the allegations of mistreatment during a meeting with his Emirati counterpart Sheikh Abdullah bin Zayed al-Nahyan, when they also expressed concern about the situation in Syria.
"We share deep concern about the escalating humanitarian crisis in Syria," Hague said.
The pair were "fully committed to bringing an end to the repression" caused by Syrian President Bashar al-Assad's "brutal regime".
Sheikh Abdullah said they discussed how to "work together to tackle the appalling humanitarian disaster in Syria".
The two also announced £1 million ($1.6 million, 1.2 million euros) each in funding to help Somalia tackle sexual violence. Britain hosts a conference on Somalia next week.
The president later visited Westminster Abbey for a short private tour along with Prince Andrew, Queen Elizabeth's second son. He laid a wreath at its tomb of the unknown warrior.
In a final engagement before leaving London, Sheikh Khalifa visited Clarence House, the official residence of Prince Charles, the queen's oldest son and the heir to the throne, at which the pair shared a light-hearted moment.
After the president eased into his chair, his translator said: "He says you have chosen him a sofa where he sinks in and it makes him look shorter."
The first day saw Sheikh Khalifa join Queen Elizabeth for a ceremonial carriage procession to Windsor Castle, west of London, where a state luncheon was held.