By Amy Kazmin in Bangkok

International aid agencies were on Sunday struggling to scale up their work in Burma as desperate survivors of cyclone Nargis poured out of the Irrawaddy delta into regional towns in search of water, food and other help.

The British charity Oxfam estimated that 1.5m Burmese are on the brink of a “massive public health catastrophe,” amid appeals for greater international access to the stricken area.

The dire warning came as Burma’s state media declared success in a referendum to secure public endorsement of a new constitution that critics say would perpetuate and legitimise military rule.

Sarah Ireland, regional director of Oxfam, told journalists Burma was facing a “perfect storm” of conditions that could lead to the outbreak of waterborne disease.

“The ponds are full of dead bodies, the wells have saline water, and even things like a bucket are in scarce supply,” she said. She appealed for Burmese authorities to permit Oxfam and other global humanitarian agencies to send technical and health experts to help prevent disease outbreaks.

Immediately after the cyclone, Burma’s rulers appealed for international help with the catastrophe. But authorities have permitted only a handful of foreign aid workers to enter the country, saying they preferred to receive supplies that the army, and the Myanmar Red Cross, which is patronised by the generals’ wives, can distribute themselves.

UN agencies, and international charities that were already operating in Burma prior to the disaster, also have been slowly setting up relief operations. Emergency supplies are gradually arriving in Burma, and filtering into the low-lying Irrawaddy Delta, but is far short of what is needed.

The World Food Programme, which on Friday accused authorities of impounding planeloads of emergency food, said their cargo – and material sent since then – had been released, and sent to the disaster zones. The International Committee of the Red Cross also sent a planeload of relief supplies on Sunday, including body bags.

Yet even a week on, most survivors have not yet received any help, due both to a lack of supplies and logistical difficulties in transporting them to the more remote parts of the delta.

Highlighting the logistical difficulties, the International Federation of the Red Cross said a boat ferrying aid to more than 1,000 survivors sank in the delta early yesterday, apparently after hitting a submerged tree.

Meanwhile, agencies operating in Burma also say that without reinforcements from abroad, their staffs have been stretched to the limit. The UN Office for the Co-ordination of Humanitarian Affairs, said the aid effort is, “still very much too piecemeal for our liking”.