The UN says 150,000 people are trapped in Sri Lanka's northern war zone while Tamils claim they are victims of human rights abuses.
Sri Lanka's government has rejected calls for a ceasefire with the Tamil Tiger rebel group, which wants independence.
Foreign Secretary David Miliband insisted the UK government was "very concerned" about civilians caught up in fighting in Sri Lanka and the need for a humanitarian ceasefire was now "even more urgent".
Meanwhile, a diplomatic row blew up over Mr Miliband's recent comment that he was disappointed Sri Lanka had rejected the appointment of former defence minister Des Browne as a special envoy.
Foreign Minister Rohitha Bogollagama said Britain had failed to adhere to the time-honoured diplomatic practice of consultation.
The illegal protest has been going on outside Parliament since 1600 BST (1500 GMT) on Monday and there are reportedly no immediate plans to end it.
Suren Surendiran, of the British Tamils Forum, said the protest had been led by students, but that people of all ages from across the UK had joined in.
"These are people who have relatives and friends in Sri Lanka; people who have lost brothers and fathers and sisters," he said.
"As British citizens, they want the UK government to act. Rather than just calling for a ceasefire, they should go to the UN security council to demand one."
Many protesters carried banners with slogans such as "Stop Sri Lanka's Genocide of Tamils".
Police have made six arrests
In recent weeks, the clashes between security forces and Tamil Tigers have intensified as the security forces enter what they say is a final push to defeat the rebels and end nearly three decades of conflict.
The United Nations says more than 2,800 civilians may have been killed and 7,000 others injured in the fighting in the north-east in the last two months. The Sri Lankan government disputes these figures.
Mr Miliband said: "Nothing excuses the reported use of civilians by the LTTE (Liberation Tigers of Tamil Eelam) as a human shield.
"But nor does the LTTE's behaviour excuse any failings by the Sri Lankan government to meet the high standards expected of democratic governments in conflict."
Leicester East MP Keith Vaz said he would deliver a letter to Downing Street on Wednesday calling for the situation to be debated by the UN Security Council, signed by a number of Labour and Lib Dem MPs.
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