The idea would make headlines around the world and bring tears of joy to the planet's journalists. An adorable baby woolly mammoth, tottering on its newborn legs, is introduced to the media. Cloned from a few cells scraped from the permafrost of Siberia, the little creature provides the latest proof of the might of modern science and demonstrates the fact that extinction has at long last lost its sting.

It is a fascinating prospect, one that was raised again last week when the most recently discovered carcass of a mammoth was revealed to the public in Yokohama, Japan.

The female, thought to have been around 50 when she died, had lain frozen in the ground for tens of thousands of years. Yet she still had hair, muscle tissue, and possibly blood. Samples have now been sent to South Korea, where scientists say they are planning to use them to clone a mammoth, though the proposal is considered to be highly controversial.

"The hunt for mammoth corpses has been transformed in recent years," said Professor Adrian Lister, of the Natural History Museum, London, and one of the advisers for the museum's current "Extinction" exhibition. "We have found as many mammoths in the past five years as we did in the previous 50, partly because global warming is melting the Siberian permafrost and is revealing more and more bodies and partly because local people realise it is a lucrative business. Mammoth ivory is viewed as a legal and ethically acceptable alternative to elephant tusks.

"The only trouble is that every time a new well-preserved mammoth is found, people also repeat the claim that we will soon be able to clone them, and I very much doubt that we will."

Mammoths ranged from the British Isles to eastern Asia and northern America until they disappeared around 10,000 years ago, though one small population was recently found to have survived to around 4,000 years ago on the Russian island of Wrangel.

Hunting by cavemen or climate change, or a combination of the two, are generally blamed for their demise.

Now some scientists are talking openly of bringing them back to life. Yokohama mammoth samples have been sent to the private laboratory of the disgraced South Korean cloning expert Hwang Woo-suk, who is co-operating with Russian scientists with the specific aim of recreating mammoths. Similarly, Semyon Grigoriev, who led the team that excavated the mammoth, has speculated that fluid found near the creature may be blood that contains intact cells which could be used to bring about their resurrection. "This find gives us a really good chance of finding living cells, which can help us implement this project to clone a mammoth," said Grigoriev.

The idea gathers little support from scientists such as Lister, however. "I very much doubt if the idea of cloning a mammoth is feasible," he said, a point that was backed by the molecular biologist Professor Michael Hofreiter, of York University.

"There are two ways that you could try to clone a mammoth," said Hofreiter. "The first is straightforward. You could simply look through the bodies we dig up in the Arctic to see if we could find one that had a cell that still contained a nucleus with a complete, viable genome in it.

"Then, employing the cloning techniques that were used to create Dolly the Sheep, we could put that nucleus inside an elephant embryo and then implant it into a female elephant, who would later give birth to a mammoth.

"The problem is that these creatures died many thousand years ago, when their DNA would have started to degrade, so the chances of finding an entire viable mammoth genome are essentially zero," he said.

There is another approach, however. Scientists could use the scraps of DNA they do find in preserved bodies to build up a map of a mammoth's genome. "Then you would use the same techniques that are employed in creating transgenic mice to make stretches of DNA – using your map as a guide – that you would then put into the embryo of an Asian elephant embryo which is the closest living relative of a mammoth," said Hofreiter.

"Bit by bit, you would continue with this process with separate pieces of mammoth DNA until you had completely replaced the DNA in your elephant embryo with mammoth DNA. You would now have an embryo with a mammoth genome it. This would then be placed in a female elephant in whom the embryo would develop to birth."

There are many difficulties with this approach, however. "A key point to remember is that elephants and mammoths each have about 4 billion DNA bases in their genomes," said Hofreiter. "However, the maximum size of the DNA section you can add is about 1 million bases. So you would have to repeat the process sequentially 4,000 times – without mishap – to create your mammoth embryo. The chances of that happening are also essentially zero." On top of these problems there is the simple issue of differences in proteins that exist between the Asian elephant that would be used as a surrogate mother and the mammoth embryo you have created. "It is quite possible that these differences would be big enough to make the embryo incompatible with the elephant. It is a further factor to suggest that mammoth cloning is not going to happen for a very long time indeed."

For good measure, there are other concerns that make the idea of cloning animals such as the mammoth controversial, added Lister.

In particular, there is the question of the ethics involved. "Mammoths were very similar to elephants, we believe," he said. "In other words, they were highly social, intelligent creatures. What right have we got to recreate one or two and then keep them in solitary confinement at zoos or research facilities? I have problems with those who think this is not a real issue."

Several other concerns also trouble scientists. Species are now being wiped off the planet at a staggering rate. The WWF has suggested a figure of around 10,000 species a year, for example, though these figures are disputed by other scientists.

The crucial point is that resources are desperately needed to help slow down the rate at which animals and plants are being rendered extinct. As a result, the idea of investing large amounts of money on reviving special interest species while the natural world is dwindling as the climate changes and human populations soar is leaving many scientists uncomfortable.

"We shouldn't be piling our cash into projects that could resurrect an already extinct large mammal," said Lister. "We should be trying to help those who are now hovering at the edge of extinction today. That would be the best way to invest our money in conservation."

Extinction: Not the End of the World? runs at the Natural History Museum London until 8 September.