David Cameron said Sri Lanka’s president has “serious questions” to answer about alleged war crimes committed by his regime, as he prepared to attend a Commonwealth summit on the island.

The British prime minister sought to increase pressure on Mahinda Rajapaksa to hold an independent inquiry into the brutal final months of the 25-year civil war with the separatist Tamil Tiger guerilla group.

He spoke out after watching what he described as a “chilling” documentary about the events of 2009, in which the United Nations believes at least 40,000 ethnic Tamil civilians were killed.

Cameron has rejected calls for Britain to boycott the Commonwealth Heads of Government Meeting (CHOGM) in protest over the failure to investigate and ongoing human rights violations in the country.

Critics say any engagement with the regime amounts to “collaboration”.

But the PM insists that his attendance – during which he will visit the north of the island to speak to affected Tamils – will help “shine a spotlight” on human rights concerns.

The documentary shows the apparent indiscriminate shelling of areas packed with civilians, including hospitals, executions and rapes by soldiers.

The regime denies responsibility for any such events.

Cameron says no-one could regret the end of the terrorist campaign waged by the Tamil Tigers who were responsible for “terrible crimes”.

“But that wrong does not change the fact that this documentary raises very serious questions that the Sri Lankan government must answer about what it did to protect innocent civilians – questions that strengthen the case for an independent investigation, questions that need answers if Sri Lanka is to build the truly peaceful and inclusive future its people deserve.”

Cameron said “positive steps” such as provincial elections and a commission to investigate the disappearances of tens of thousands of people fell well short of what was required.

“I will raise my concerns when I see President Rajapaksa next week in Colombo,” he said.

“And I will tell him that if Sri Lanka doesn’t deliver an independent investigation, the world will need to ensure an international investigation is carried out instead.”

The prime minister has said it looks “increasingly unlikely” that Mr Rajapaksa will comply.