The ethnic Tamil community in Britain numbers around 250,000 to 300,000 people and in recent weeks it has organised several large protests in London to put pressure on the British government, the former colonial power in Sri Lanka, to act.
Suren Surendiran, one of the organisers from the British Tamils Forum, described the situation in Sri Lanka as "genocide".
"Our first demand is that we want the government to get a resolution at the UN to implement a ceasefire so that the war can stop," Surendiran said.
"The second demand is to send in humanitarian aid and medical supplies.
"And the third demand is for independent journalists and international NGOs [non-governmental organisations] to be allowed into the area to see directly what is happening."
Two demonstrators have been on hunger strike since Tuesday.
One stopped his protest on Saturday after being offered the opportunity to take his case to the UN, while the other agreed to take liquids after doctors warned he faced renal failure.
Protests were also held in the capitals of France, Norway and Denmark on Saturday.
Sri Lanka's government says it is in the final stages of defeating the LTTE, who have been fighting for an independent homeland in the north and east of the country since 1972.
The LTTE is listed as a banned "terrorist" group by the British government.
According to the UN, more than 2,800 civilians may have been killed in the conflict in northern Sri Lanka in the last two months alone.
The government rejects the figure, and any accusation of targeting civilians.
About 100,000 civilians are believed to be effectively trapped between the army and the LTTE in a "no fire" zone - a 20sq km coastal strip that the military says it established to provide a place of refuge to people caught up in the fighting.
The government accuses the Tamil Tigers of trapping the civilians so they can be used as human shields, while the LTTE says the military has repeatedly shelled the "no fire" zone.