Three Londoners, including 25-year-old Indian-origin Suneet Jeerh, have claimed they were subjected to beatings and electric shocks since their arrest in Dubai in July 2012.
Cameron is set to hold talks with Sheikh Khalifa bin Zayed al-Nahyan, head of state of the UAE, at his Downing Street office today, the second day of a two-day state visit to Britain.
The trio were jailed for four years each on charges of possessing synthetic cannabis or "spice" earlier this week and their families have urged the UK government to intervene.
Cameron, however, also stressed on the "good relationship" the two countries share.
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"We have a very good relationship with the UAE. I am delighted that they are here on the state visit this week. 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.
Jeerh's family, alongside those of his friends Grant Cameron and Karl Williams, has been urging for the government to push for their release during the high-profile state visit.
Sheikh Khalifa, who was in Windsor Castle to visit Queen Elizabeth II yesterday, sat alongside her for a ceremonial carriage procession to the castle where a state luncheon was held. He will also visit Westminster Abbey for a short private tour along with Prince Andrew, the Queen's second son.
Britain normally stages two state visits a year, aimed at strengthening the relationship with the visiting country. The last state visit from the UAE was in 1989.