Cetti's warbler is not alone – the little egret has now colonised Britain, which had previously been too cold for the bird; and the comma butterfly can now be found in Edinburgh, at least 220 kilometres north of its former central England home.

These changes, in response to global warming, have happened two to three times faster than was previously expected, according to a new study from the biology department of York University, published on Thursday evening in the peer review journal Science. Although such responses to global warming have been predicted, the study is the first to show that animal and plant species have moved furthest in the regions where the climate has warmed the most.

Species have tended to move towards the poles, fleeing in search of their more accustomed temperatures as climate change has resulted in warming of their normal habitats, according to the new research. The phenomenon is one of the clearest examples of climate change in action.

Chris Thomas, professor of conservation biology at York University and leader of the project, said: "These changes are equivalent to animals and plants shifting away from the equator at around 20 centimetres per hour, for every hour of the day, for every day of the year. This has been going on for the last 40 years and is set to continue for at least the rest of this century. "

The research team analysed data from a variety of studies, most of them from Europe and North America, finding more than 2,000 examples of how animal and plant species have adapted by moving their habitat. They found that, on average, species have moved to higher ground at a rate of 12.2 metres per decade, and moved closer to the poles at the faster speed of 17.6 metres per decade.

Thomas said: "This study [which shows] for the first time showed that species have moved furthest in regions where the climate has warmed the most, unambiguously links the changes in where species survive to climate warming over the last 40 years."

A moth that was found to have moved 67 metres uphill on Mount Kinabalu in Borneo showed that vast changes to the climatic system are borne out in the beating of an insect's wing.

Species are being forced to move in order to stick to the temperatures that they have evolved to expect. But the study also found wide variations among different species. For instance, some northern hemisphere species have moved south, and others have not moved at all. The scientists said this could be owing to the influence of other changes to the environment, independent of climate change – such as dwindling habitat, and a response to predators.

One example is the high brown fritillary butterfly, which in the UK might have been expected to move – along with some other butterfly species – northwards into Scotland. But populations of the butterfly have declined, because its normal habitats have been lost. And while Cetti's warbler – a small brown bird that belies its loud song – moved northwards, the cirl bunting moved south within the UK by 120km, a victim of intensified agriculture.

Birds and butterflies may tend to be more mobile, but mammals, reptiles, spiders, insects and all sorts of invertebrates were also tracked.

Previous studies have also found that climate change could represent a serious extinction risk to at least a tenth of the world's species. Thomas said: "Realization of how fast species are moving because of climate change indicates that many species may indeed be heading rapidly towards extinction, where climatic conditions are deteriorating. On the other hand, other species are moving to new areas where the climate has become suitable, so there will be some winners as well as many losers."