Most of the deaths are the result of waterborne diseases, particularly diarrhoea, the paper said, quoting a senior relief worker it said spoke on condition of anonymity.
Women, children and the elderly were shoved aside in the scramble for supplies, it said.
Long queues
The Menik Farm camp, in the northern district of Vavuniya, was set up to house the largest number of the 300,000 mainly Tamil civilians forced to flee the northeast as the military mounted an offensive against the Liberation Tigers of Tamil Eelam (LTTE).
The government announced victory over the LTTE in May, ending a civil war that lasted decades.
The Times said witness testimonies it obtained in May described long queues for food and inadequate water supplies inside the camp.
Women, children and the elderly, it said, were shoved aside in the scramble for supplies.
Aid agencies are being given only intermittent access to the camp. The International Committee of the Red Cross (ICRC) was not being allowed in, The Times reported.
Toll controversy
The Times also said that its investigation had uncovered evidence that more than 20,000 civilians were killed, mostly by the army, in the final stages of the conflict.
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| The Times said women and children are pushed aside in the scramble for food [AFP] |
But Sri Lankan doctors said at a news conference on Wednesday that they had deliberately overestimated the civilian casualties.
As government officials looked on, they claimed that the Tigers had forced them to lie, The Times reported.
Mangala Samaraweera, a former foreign minister and now an opposition MP, told Al Jazeera the Sri Lankan president has been "duplicitous in his dealings as far as the ethnic question is concerned".
"The all-party conference has been and still is merely a piece of theatre to keep Indian pressure and, of course, international pressure at bay and nothing has yet to come out," he said.
"It is nearly two months since the defeat of the LTTE, but the government has yet to come up with a political solution, which is acceptable to the minorities in this country."
Situation 'improving'
But Rajiva Wijesinha, secretary at the Sri Lankan ministry of disaster management and human rights, said that the situation in the camps was improving.
"The conditions are much better than they were about a month ago," Wijesinha said.
"Things are getting much better ... With regard to resettlement the actual programme of developing the north in terms of demining as well as with regard to infrastructural development is going quite well.
"But we do have to make sure that all is done properly and we cannot resettle [displaced people] without certificates as we did in the east."
The Times reported, quoting the ICRC, that the agency was closing two offices in the country.
One of these was in Trincomalee, which had helped to provide medical care to about 30,000 injured civilians evacuated by sea from the conflict zone in the northeast, the report said.
The other was in Batticaloa, where the ICRC had been providing "protection services".
The ICRC has revealed that it has been asked to scale down its operations by the Sri Lankan authorities, who insist that they have the situation under control.