Would you like a farm with that? In addition to snapping up multimillion-pound townhouses in Knightsbridge and Chelsea, rich foreigners are now buying farms and country estates across the UK.

Estate agents are reporting a big increase in investment buyers – some from as far away as China – trying to buy swaths of British farmland. The influx has sent the price of farmland to a record high of £6,882 an acre – an 11% jump on this time last year and a 210% increase over the past decade.

Andrew Shirley, head of rural research at estate agents Knight Frank, said: "People from around the world who buy a townhouse in Chelsea look around for what else they could buy … increasingly they're looking at country estates and farmland. There has been a significant increase in inquiries from overseas investors."

Knight Frank had sold to South Africans, Scandinavians and "a lot of Italians", he said. "We're even showing Chinese people around farmland."

He said rich buyers were "not going to be sitting on the tractors themselves" but were buying farms for investment or as a "lifestyle estate".

Shirley said Scandinavians had long been keen on grouse-shooting and salmon-fishing estates in Scotland, while Middle Eastern racing fans were buying up stud farms around Newmarket, Suffolk.

The Chinese are also becoming increasingly attracted to the British countryside, though more for its investment potential than to be country squires.

Rich buyers spent £54m on Scottish estates last year, according to the estate agency Savills. One world-renowned grouse-shooting estate changed hands for £20m and two others sold for between £8m and £10m.

Evelyn Channing of Savills' rural office said sporting estates had been "at the top of Christmas wish lists" for international businessmen and women. Channing is in the midst of selling a nine-bedroom castle set in 10,000 acres of deer-stalking woodland. She said the Cluny estate, which dates back to the 1600s and is on the market for £7.5m, was very likely to be sold to a foreign buyer. Two-thirds of potential buyers had been from Scandinavia, particularly Denmark.

The estate, near Kingussie in Inverness-shire, is being sold by the Egyptian-born, Norwegian-based telecoms magnate Alain Angelil, 70, who is reported to have bought the estate, which includes 10 outbuildings, for £2.7m in 2001.

Channing said the asking price for country estates had rocketed because only four or five reach the market a year, but arable land was experiencing exceptionally strong demand.

Research by Knight Frank shows the average price of UK farmland has risen to £6,882 an acre, compared with £6,214 a year ago. That works out as an 11% increase, compared with an 8% increase in UK average house prices and a 30% decrease in the price of gold over the same period. The 210% rise in the price of farmland over the past 10 years is significantly more than that for the FTSE 100 – the index of leading shares has risen by 51%.

"People are seeing the long-term growth of farmland, and realising it could be a good thing to add to their portfolio," Shirley said. "It's not likely to disappear, and it provides a good yield."

Before the credit crunch a lot of investment funds were buying up farmland but now it was mostly rich individuals, Shirley said. "Investors are looking for good-sized blocks, ideally 1,000 acres of good arable land in East Anglia," he said. "People are willing to pay £8,000-£10,000 an acre for the best sites. And a lot changes hands for a lot more privately."

Ian Bailey, the head of rural research for Savills, said prices were rising because demand far outstripped supply. Last year just 150,000 acres of farmland were put up for sale compared with 300,000 a decade ago.

"It's a tangible asset – people can live on it and walk on it," he said. "It's a popular product and we're not making more of it."

The agents said buyers are also attracted by the increasing array of money-making opportunities from land ownership, which now extends to rent from wind turbines and fracking as well as traditional farming activities.

"You can see that the government is pretty keen on fracking," Shirley said. Although landowners cannot collect mineral rights like in the US, they can charge for access for drilling. "Fracking could be a useful additional income, but you're not going to become a Texan oil magnate."

He said there was more potential in wind turbines, which could be "very lucrative". "There are a lot of people making lots of money from wind turbines," he said.