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Cameron has said he wants a "proper, independent investigation" into the allegations of police mistreatment.
The three Londoners in their 20s, jailed for four years each on drugs charges, were subjected to beatings and electric shocks, campaigners have claimed.
"The point I will make today is that we think there needs to be a proper, independent investigation into these allegations of what happened," Cameron told ITV television.
"That is the first step really of working out what needs to happen next."
He said Britain had a "very good relationship" with the UAE.
"We have very deep economic and trading relations and we have also got over 100,000 British people who choose to live in Dubai and Abu Dhabi.
"So our countries are very close but nothing should be off limits in these discussions."
The mother of one of the men, Grant Cameron, welcomed the prime minister's intervention but said she hoped he would go further in the talks.
"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.
She said the case had been a "catastrophic" experience for the families of the three young men, but was "very confident" progress could be made.
On Wednesday Sheikh Khalifa will also visit Westminster Abbey for a short private tour along with Prince Andrew, the queen's second son.
He was to lay a wreath at its tomb of the unknown warrior.
The president was then to visit Clarence House, the official residence of Prince Charles, the queen's oldest son and the heir to the throne.
Britain and the UAE on Wednesday announced £1 million ($1.6 million, 1.2 million euros) each in funding to help Somalia tackle sexual violence.
Britain, which is hosting this year's Group of Eight summit, is making combating sexual violence in conflict zones a priority.
It will also be raised at a major London conference on Somalia on Tuesday.
Emirati Foreign Minister Sheikh Abdullah bin Zayed al-Nahyan said: "Through this contribution, the UAE is delighted to be able to support the Somali government in its efforts to protect and empower women."
At the start of the visit on Tuesday, Sheikh Khalifa sat alongside the queen for a ceremonial carriage procession to Windsor Castle, west of London, where a state luncheon was held.
Britain normally stages two state visits per year, aimed at strengthening the relationship with the visiting country.
The last state visit from the UAE was in 1989.
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The three Londoners in their 20s, jailed for four years each on drugs charges, were subjected to beatings and electric shocks, campaigners have claimed.
"The point I will make today is that we think there needs to be a proper, independent investigation into these allegations of what happened," Cameron told ITV television.
"That is the first step really of working out what needs to happen next."
He said Britain had a "very good relationship" with the UAE.
"We have very deep economic and trading relations and we have also got over 100,000 British people who choose to live in Dubai and Abu Dhabi.
"So our countries are very close but nothing should be off limits in these discussions."
The mother of one of the men, Grant Cameron, welcomed the prime minister's intervention but said she hoped he would go further in the talks.
"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.
She said the case had been a "catastrophic" experience for the families of the three young men, but was "very confident" progress could be made.
On Wednesday Sheikh Khalifa will also visit Westminster Abbey for a short private tour along with Prince Andrew, the queen's second son.
He was to lay a wreath at its tomb of the unknown warrior.
The president was then to visit Clarence House, the official residence of Prince Charles, the queen's oldest son and the heir to the throne.
Britain and the UAE on Wednesday announced £1 million ($1.6 million, 1.2 million euros) each in funding to help Somalia tackle sexual violence.
Britain, which is hosting this year's Group of Eight summit, is making combating sexual violence in conflict zones a priority.
It will also be raised at a major London conference on Somalia on Tuesday.
Emirati Foreign Minister Sheikh Abdullah bin Zayed al-Nahyan said: "Through this contribution, the UAE is delighted to be able to support the Somali government in its efforts to protect and empower women."
At the start of the visit on Tuesday, Sheikh Khalifa sat alongside the queen for a ceremonial carriage procession to Windsor Castle, west of London, where a state luncheon was held.
Britain normally stages two state visits per year, aimed at strengthening the relationship with the visiting country.
The last state visit from the UAE was in 1989.
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