Less than a fifth of the £650m urgently needed for the Horn of Africa has been pledged, Oxfam said, with the response from most of Europe "surprisingly slow".
"There has been a catastrophic breakdown of the world's collective responsibility to act," said Fran Equiza, Oxfam's director in the Horn of Africa.
"Several rich governments are guilty of wilful neglect as the aid effort to avert catastrophe in East Africa limps along.
"The warning signs have been seen for months, and the world has been slow to act. By the time the UN calls it a famine it is already a signal of large scale loss of life."
Aid agencies have taken out full-page advertisements in newspapers and launched appeals on television and radio, as 11 million people across Kenya, Ethiopia and Somalia face the threat of starvation.
In Britain, more than £21m has been donated by private individuals, and the Government has promised £90m in fresh funds for drought relief.
"It is time for the world to help but sadly the response from many countries has been derisory and dangerously inadequate," said Andrew Mitchell, the International Development secretary. "Britain is playing its part, with help for more than two million people across the Horn of Africa. Now others must do the same." European Commission figures show that Britain is already the largest funder of European aid projects to Somalia, pledging £24m in 2011 even before the current crisis hit.
Sweden, the next largest EU donor, gave £11m. Germany has promised £4.3m in new money for the current crisis, and Spain has made what Oxfam called "an initial contribution".
Japan said yesterday that it was donating £3.2m to the appeal. Aside from Kenya, Ethiopia and Sudan, no African country has offered any funds.
France was "strong on words", Mr Equiza said, but had not promised any funding at all for the drought appeals.
The US announced a fresh injection of £18m yesterday, to buy food mostly for Somali refugees in Kenya and Ethiopia, and for people in the country's north.
Mark Bowden, the head of the UN's operations in Somalia, said as he announced the first official famine in Africa since Live Aid that "tens of thousands" of people had already died.
"I'm not going to say it's not going to deteriorate further, it will," he said in Nairobi, Kenya's capital and the headquarters of the aid effort across the Horn of Africa.
"Even if the world starts acting as must, now, lives will be lost. But there are many more lives that can be saved if we see the level of response that is desperately needed."
Aid workers point out that weather reports and famine early warning systems operating in Somalia had predicted extreme shortages of food as long ago as January.
"The announcement of a famine across much of east Africa is as tragic as it is predictable," said Jeremy Hulme, chief executive of the Society for the Protection of Animals Abroad.
The single biggest factor in tipping people in the Horn of Africa towards famine has been the loss of their livestock, their only source of food, wealth and income.
"It's scandalous that we're seeing this avoidable tragedy unfolding across the region," Mr Hulme added.
"Once again our belated response is a vast operation to feed the starving, having failed to protect their livelihoods."