Major food price rises are all but inevitable, the chief executive of Britain's biggest supermarket chain has admitted. Speaking exclusively to the Observer, Philip Clarke of Tesco, which was heavily implicated in the horsemeat scandal, said that rising global demand means the historic low prices to which British consumers have become used are now unsustainable.

"Over the long run I think food prices and the proportion of income spent on food may well be going up," he said. "Because of growing demand it is going to change. It is the basic law of supply and demand." The admission comes as a new poll, commissioned by the Prince's Countryside Fund to mark National Countryside Week beginning tomorrow, reveals that a majority of British consumers would be prepared to pay more for food if they knew the extra was going to farmers rather than to supermarket shareholders. The YouGov poll also indicates that more than 80% of consumers think it is important to buy British produce where possible as a way of showing support for the nation's farmers.

"The British public care deeply about British agriculture and are prepared to support British farmers, even if that means paying more for food, provided that extra money returns directly to the producer," said Donald Curry, a trustee of the Prince's Countryside Fund, which was founded by the Prince of Wales in 2010 to support struggling farmers and the rural way of life. "Farmers play a vital and important role not just to the rural economy but in managing the countryside."

The United Nations Food and Agriculture Organisation forecast last month that global food prices could rise by as much as 40% over the next decade, as a result of a growing middle class in countries such as China and India. However, Britain's supermarket bosses have proved extremely resistant to admitting economic pressures would affect the cost of groceries shopping. Previously only Mark Price, chief executive of Waitrose, has broken ranks by admitting food price inflation is inevitable, although his affluent customer base is regarded as being less price sensitive. Last month food price inflation rose slightly from 2.4% in May to 2.7% in June.

In February, Philip Clarke told a conference of the National Farmers Union that Tesco would source more of its produce from Britain and give better deals to farmers, in an attempt to restore trust in the brand following the discovery of horsemeat in four of the supermarket's beef products. At the time he insisted the initiatives did not mean "that food needs to become more expensive". However, during the Observer's interview he admitted that while price is important "it's not everything. We're working very hard with our buyers so they're not just focused on price."

In a wide-ranging interview Clarke confessed that, in the wake of both the horsemeat scandal and a slump in pre-tax profits by more than 50%, the retailing giant, which has a 30% share of the food market, had still to regain the public's trust. Its own research revealed that the public thought "Tesco was big and Tesco was bad".

He said the company, which employs 325,000 people in the UK and has a global turnover of nearly £75bn, is determined to do all it can to keep food price rises in check, by giving farmers better contracts so they can invest in the agricultural base. "We've got to produce more food at home and we've got to make better deals with producers," he said.