Amos Mwesige looks across the 15 metres of swirling water to the opposite bank with a mixture of frustration, anger and defiance. He is angry because the river's changing course has taken his land and delivered it to a man on the other side – a man who lives in another country.

"The land where our grandparents used to cultivate – it is now in Congo. It is now being controlled by [the Congo government]," says Mwesige, a farmer and cattle herder in Kabimbiri in western Uganda. "I have to go and kneel before them: Congo's leadership."

Worse, he now has to pay one cow per year in rent for the privilege of cultivating the crops on the land he used to own. All he wants is the return of the farm that he sees as his birthright.

Mwesige is far from alone in his plight. Increased flooding of the Semliki river in recent years has led to major shifts in its course. It is just one example of the way changes in the local weather patterns are affecting people in the region: with the changed seasons, farmers no longer know when to plant and harvest; diseases such as malaria are spreading into new areas; and the moving river means that Uganda is shrinking.

It is problems such as these that are an integral part of current international climate negotiations in Cancún in Mexico that will reach their climax on Friday. Although politicians have been frantically playing down expectations for the talks after the limp outcome of last December's gathering in Copenhagen, many observers are hopeful of progress on aid funding for poorer nations to help them adapt to climate change. On the table is a proposal from a group of economists, finance ministers and heads of state on how to raise $100bn a year by 2020. The plan – to be discussed by ministers at the UN climate talks today – combines carbon taxes, aviation and shipping taxes, and the redirection of fossil fuel subsidies.

John Magrath, a climate change researcher with Oxfam, believes the plight of people such as Mwesige shows how vulnerable much of the population in the region is to any change in the climate. "For generations, they have relied on fairly set weather patterns and an environment that has served them well, but now they are undergoing great change and heightened risks to their health, security and welfare."

International action on climate change has so far been characterised by a "pathetic lack of urgency", he says, and governments must make amends for failing to reach a substantive deal at Copenhagen. "The longer the inaction, the harder it is for people like those in Uganda to begin to protect themselves from its effects."

For the time being, Mwesige and his fellow farmers are on their own. They refer to the river "eating" the land, and although the change in the river has taken sections of bank from both sides, it is Ugandan farmers who have lost out the most. Because the river forms the official border between Uganda and the Democratic Republic of the Congo (DRC), the boundary between the two countries has moved with it, meaning Uganda has got smaller.

There is seething resentment in the community. "I feel suppressed and squeezed," says Francis Mwhanuzi, another farmer. "I'm meant to pay 50,000 shillings [£14] and a goat [in rent] but still I remain with a broken heart because of losing my land."

Both men sometimes opt not to make the boat trip across to their farms for fear of violence. "At times Congo has a very big problem, it is politically unstable," says Msesige. "At times we fear to go to our gardens because of civil war." The border region is riddled with ethnic tensions and is still traumatised by the 1998 to 2003 war in the DRC which brought bloody incursions by Congolese fighters from a rebel group called the Allied Democratic Forces (ADF). The Ugandan side is still dotted with army encampments housing troops that patrol the area.

"People were forced out of their homes, their communities and settled in camps," says Bernard Tumwebaze, Oxfam's programme manager in the region. "That led to devastation of their livelihoods."

Some fear the small-scale border disputes caused by the moving Semliki river could spark violent clashes once again.

Jackson Bambalira, the chairman of the Bundibugyo district, the local government office with responsibility for the area, says though there had not been any violence so far, Congolese officials had reneged on a deal struck with his administration. "[They] betrayed our agreement by which the Ugandans could get their food without interference . . . they said: 'This is our country, you cannot control us.'"

And the precise position of the border is set to become even more important: both countries are prospecting for oil on either side of the river close to where it flows into Lake Albert.

The surging waters of the Semliki river originate from the rain and snow falling on the vast Rwenzori mountains, an epic range just a few miles north of the equator that rises to over 5,100m. The snowy peaks have changed rapidly in the last 100 years or so, almost certainly as a result of the increase in global temperatures caused by human greenhouse gas emissions. It is the changes to the climate on the mountains – and the heavy rainfall that come with it – that is partly to blame for the shifts in the river on the vast plain below.

"I remember when I was in primary school, my school teachers would tell us to go outside our classrooms so that we could look at Margerita and other snow-capped peaks on the Rwenzori mountains," says Dr Clovis Kabaseke, an environmental scientist at Mountains of the Moon University in Fort Portal, the regional centre. "It was quite a sight and we were very proud of it – having snow on the equator. These days you can go out a thousand times and you will never see the snow at all. And this is just in a lifetime."

When the mountains were first charted by the mountaineer and explorer Prince Luigi Amedeo of Savoy-Aosta, Duke of the Abruzzi, in 1906, the peaks had 43 glaciers distributed over six mountains. Now, only three mountains are topped with ice, and the area covered by ice has plummeted from 650 hectares to 148 hectares.

"They are very visibly melting," says Dr Richard Taylor, a hydrogeologist at University College London. A study by him, the World Wildlife Fund and the Uganda Wildlife Authority estimates that the remaining glaciers will melt entirely by 2025.

But the melting ice contributes a relatively small amount of water to the Semliki river. It is the more erratic rainfall in recent years, the increase in heavy downpours, and over-grazing of the river banks that are causing the river to flood and change course. It is difficult for climate scientists to be sure that these more localised weather changes are caused by the global phenomenon of warming caused by human activities, but they are having a profound effect.

"Climatic changes have been very evident here in Uganda," says Kabaseke. "Especially, we get longer droughts than we expect and when we have the wet seasons they are wetter than we expect – causing rivers to burst their banks, causing landslides and very many natural disasters."

Mwesige and the other local farmers know little of the negotiations between government ministers and heads of state who are meeting to discuss their future in Cancún, but they are taking action to try to prevent the Semliki from encroaching further. Local people, along with the district government and the National Environment Management Authority, have created a fenced-off strip of land along the bank 100m wide and 5km long. The idea is to keep out cattle which have badly over-grazed the bank, leaving it vulnerable to erosion. This appears to be helping. The exclusion zone is a lush green oasis of shoulder-high grasses and shrubs all holding the earth together with their roots – a stark contrast to the cracked bare mud left by the trampling cows.

Unless the river moves back to its original course, Mwesige knows he is unlikely to get his farm back. But he hopes that by securing the bank at least his community and his country will not have to give up any more of their birthright to the fickle waters.

• The flights and accommodation for James Randerson's trip to Uganda were paid for by Oxfam. The charity did not have any control over content of the article.