The world's food crisis, where 1 billion people are already going hungry and a further 2 billion people will be affected by 2050, is set to worsen as increasing heatwaves reverse the rising crop yields seen over the last 50 years, according to new research.

Severe heatwaves, such as those currently seen in Australia, are expected to become many times more likely in coming decades due to climate change. Extreme heat led to 2012 becoming the hottest year in the US on record and the worst corn crop in two decades.

New research, which used corn growing in France as an example, predicts losses of up to 12% for maize yields in the next 20 years. A second, longer-term study published on Sunday indicates that, without action against climate change, wheat and soybean harvests will fall by up to 30% by 2050 as the world warms.

"Our research rings alarm bells for future food security," said Ed Hawkins, at the University of Reading, who worked on the corn study. "Over the last 50 years, developments in agriculture, such as fertilisers and irrigation, have increased yields of the world's staple foods, but we're starting to see a slowdown in yield increases."

He said increasing frequency of hot days across the world could explain some of this slowdown. "Current advances in agriculture are too slow to offset the expected damage to crops from heat stress in the future," said Prof Andy Challinor, at the University of Leeds. "Feeding a growing population as climate changes is a major challenge, especially since the land available for agricultural expansion is limited. Supplies of the major food crops could be at risk unless we plan for future climates."

Hawkins, Challinor and colleagues examined how the number of days when the temperature rose above 32C affected the maize crop in France, which is the UK's biggest source of imported corn. Yields had quadrupled between 1960 and 2000 but barely improved in the last decade, while the number of hot days more than doubled.

By the 2020s, hot days are expected to occur over large areas of France where previously they were uncommon and, unless farmers find ways to combat the heat stress that damages seed formation, yields of French maize could fall by 12% compared to today. Hawkins said there will be some differences with other crops in different locations, but added: "Extreme heat is not good for crops."

The second study is the first global assessment of a range of climate change impacts, from increased flooding to rising demand for air conditioning, of how cutting carbon emissions could reduce these impacts, published in Nature Climate Change. "Our research clearly identifies the benefits of reducing greenhouse gas emissions – less severe impacts on crops and flooding are two areas of particular benefit," said Prof Nigel Arnell of the University of Reading, who led the study, published in Nature Climate Change.

One example showed global productivity of spring wheat could drop by 20% by the 2050s, but such a drop in yields is delayed until 2100 if firm action is taken to cut greenhouse gas emissions.

River flooding was the impact which was most reduced if climate action is taken, the study found. Without action, even optimistic forecasts suggest the world will warm by 4C, which would expose about 330m people globally to greater flooding. But that number could be cut in half if emissions start to fall in the next few years. Flooding is the biggest climate threat to the UK, with over 8,000 homes submerged in 2012.

Another dramatic impact was on the need for air conditioning as temperatures rise. The energy needed for cooling is set to soar but could be cut by 30% if the world acts to curb emissions, with the benefit being particularly high in Europe. However, climate action has relatively little effect on water shortages, set to hit a billion people. Just 5% of those would avoid water problems if emissions fall.

"But cutting emissions buys you time for adaptation [to climate change's impacts]," said Arnell. "You can buyfive to 10 years [delay in impacts] in the 2030s, and several decade from 2050s. It is quite an optimistic study as it shows that climate policies can have a big effect in reducing the impacts on people."

Ed Davey, the UK's secretary of state for energy and climate change, said: "We can avoid many of the worst impacts of climate change if we work hard together to keep global emissions down. This research helps us quantify the benefits of limiting temperature rise to 2C and underlines why it's vital we stick with the UN climate change negotiations and secure a global legally binding deal by 2015."