Just as the books had indicated, he found a disused mining area that still contained monster diamonds, 'as big as hazelnuts, so far up to 16 carats'.
The polite and reticent Mr Jeffcock, 6ft 1in, tanned and dressed in a Harris tweed jacket and faded jeans, resembles the Edwardian gentleman-expatriate of Imperial times. His facial scar is from an old injury inflicted in India. While in London visiting his youngest son and father, he was prospecting again last week at the British Museum.
'I have located gold and diamonds that way,' he says, sipping a rare gin and tonic after a month on his diamond camp, which is dry. 'This time I hope it will be South American emeralds. An amateur history enthusiast can be as successful in locating precious metals and gemstones as a geologist. All you need is a readers' ticket to the British Museum. Most rich deposits of precious minerals have been worked before, hundreds of years ago - even thousands - so most mines are on maps.'
Acting on his conviction that high-grade deposits can be located without geologists - though they may be needed to evaluate a quarry - he has located mines that have been abandoned because of politics, wars, economics, companies going bankrupt or transferring operations to newer sites. Many are waiting to be re-worked. 'In South America dozens of gold and silver diggings are overgrown with shrubs and weeds. Last century, when local labour forces were nearly wiped out by European-introduced smallpox, mines were deserted.'
Mr Jeffcock has the slight accent of someone who has spent much of his life in different places, usually abroad. He was born in Littlehampton, West Sussex, but his childhood homes were on the Isle of Wight, followed by India - when his Yorkshire father became deputy director of civil aviation in Delhi - and Pakistan. School was Bedales in Hampshire, university Madrid. Before he was 30, he owned the Atholl Gallery in Mayfair, which specialised in early 19th-century oils and watercolours. After his marriage broke up in 1970 he made a fresh start in Dallas with another gallery, again specialising in 19th-century paintings.
'A friend in Dallas told me that while they were drilling for oil in Ecuador Indians kept offering to sell them large quantities of gold panned from river beds. In a newspaper I read about the major gold mines in Peru and Columbia being known to the Spaniards; I researched neighbouring Ecuador in a library. From 1902 to 1986 only the government had been allowed to mine there. So there had been no activity for decades.'
By then an unmarried man, Mr Jeffcock was undaunted at the idea of yet another new country. Travelling light because of a back injury, he arrived in Quito in December 1986 to claim a lease, burdened only with his first magnifying glass, working compass and sieve. In 1990 he sold his interest in the lease at a huge profit.
To celebrate the sale, he flew back to London, where at a nightclub he met someone who gave him a book on the history of the diamond industry. 'I hadn't finished the book before I applied for a reader's ticket at the British Museum,' he says. 'They made me write a letter explaining my interest in old maps. Also I bought two maps, one at the Map House in Beauchamp Place (it has now moved) and one from a shop in Lowndes Square which is now closed.'
Mr Jeffcock found where diamonds were discovered in Coromandel around 1850 and why the mines had been abandoned. In the 1870s they become uneconomic as huge quantities of diamonds found in South Africa caused a catastrophic fall in prices. .
'With the old maps and scribbled sketched copies in my briefcase, I flew to San Paulo, then on to Uberlandia, south of Brasilia, and then by car to Coromandel. Although the area targeted was being farmed for coffee and cattle, there were a few dozen illegal miners using primitive hand tools.'
He went to check the Coromandel area in the Department of Mines in Brasilia. 'I found that large diamonds, such as the President Vargas 726.6 carat, came from there,' he says proudly. 'The number of pink diamonds recovered there is fabulous - some are like the one the Queen received as a wedding present.'
Mr Jeffcock tried to buy the mining lease, but the proprietor in Rio was reluctant to sell. However, when bank accounts in Brazil were frozen to curb inflation - withdrawals were limited to a few hundred dollars - he went to Dallas, stuffed his briefcase with dollars 118,000 and returned to Rio to buy the leases for 12,500 acres. Merging with another company which had spent dollars 1.5m on development and machinery along the Rio Santo Inacio, 500 miles due north of Sao Paulo, he brought in equipment and built a small village for 60 workers.
'Life is mainly hard work,' he says. 'There is no cinema, and TV reception is appalling. But there is mains electricity, and there's good fishing, especially of piranhas, which are delicious grilled.'
Now, three years later, Mr Jeffcock's Rio Santo Inacio Mine is processing 200 lorryloads of gravel a day, and producing about 300 carats of diamonds a week.
William, 30, the eldest of Mr Jeffcock's three sons, manages the mining camp of welders, two cooks, two geologists, mechanics, drivers, heavy machinery operators and miners. There are just two women: a geologist from London and a local cook.
'The moment I mention Brazil, people assume we are chopping down trees in the Amazon,' Mr Jeffcock says. 'We are thousands of miles from any jungle and the land has been ploughed in the past. We use no acids or chemicals in the recovery of diamonds which, luckily, are alluvial, so we only go down to bedrock. We replant where we have mined with trees or grasses.'
He scoffed at the idea of diamond mining being risky, with the Russians flooding the market. 'Russian production is down by 25 per cent and stones from Angola have virtually ceased because of the civil war. The large size of many of our diamonds means we are less affected by market trends, but for the first time for three years demand is outstripping supply.
'De Beers' Central Selling Organisation (which controls 80 per cent of the world market in rough diamonds) raised the price of diamonds by about 1.5 per cent a few weeks ago. The world retail diamond market of dollars 40bn is growing.'
Britain has superb reference libraries, says Mr Jeffcock, but he thinks they should be more practical. 'There are no diamond exploration companies listed on the London Stock Exchange. In contrast, there are more than 50 diamond exploration companies listed on the various Canadian exchanges, which is why we are listed there and not London.'
He stresses that more gems are waiting to be found by amateurs. All they need is the courage to brave the stern silence of places - such as the British Museum Reading Room.
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