It was summer 1956, shortly after Jim Laker had taken all ten Australia wickets at Old Trafford to retain the Ashes, and a young English boy who had always supported Australia was trying to rewrite history in his garden.

After much running up and down, bowling at stumps, Richard Robins went inside and proudly announced to his father's friend, who was visiting from Australia, that he had just taken ten wickets and beaten England. The friend was so amused that when he returned to Australia he sent the child, his godson, an item of clothing. It came with a note that read: “On his twelfth birthday, I gave Richard Robins one of my Aust. XI caps” and was signed Don Bradman.

More than half a century on, that cap is expected to be sold at auction in Melbourne on December 15 for a record sum that could be as high as A$750,000 (about £325,000). Global financial crisis or not, Bradman memorabilia attracts big money.

Walter Robins, Richard's father, was a former England all-rounder once described by Bradman as his “best pal in the cricket world”. He played 19 Tests in the 1930s, captaining England against New Zealand in 1937, and once bowled Bradman with a googly at Trent Bridge in 1930.

The Baggy Green cap was worn by Bradman during the 1948 tour to England, his last, when the Australia squad known as “The Invincibles” won 23 and drew eight of its 31 matches, 15 of the wins being by an innings. Bradman had been uncertain about touring and was persuaded by Robins, who told him that his presence would cheer up the country in its postwar depression.

Bradman was swayed by the argument, replying to Robins in a letter that is included in the auction with the cap that sentiment alone was taking him to England. He made two hundreds in the Test series, but his career batting average slid below 100 when he was dismissed for a duck in his last innings by Eric Hollies.

In 2003 the cap was sold by Robins for A$425,000 to Tim Serisier, a banker from New South Wales, who used A$250,000 that he had won on the Australian Who Wants to be a Millionaire television quiz. He loaned it to the National Sports Museum in Melbourne but has decided to cash it in. “Something of that value, I think it's time for somebody else to take it on,” Serisier said.

He added that he had never been tempted to wear the cap. “That's always been a rule of mine,” he said. “That would really be a bit rude.”

Charles Leski, the auctioneer, said: “This is the single most valuable item we've ever auctioned - sporting, Australiana, across the board.” The cap has a reserve price of A$450,000 but an estimated sale price of A$600,000-$750,000.

The Baggy Green cap is a sporting icon to many Australians. Mark Taylor and Justin Langer are believed to have used only one cap in more than 100 Tests, but in Bradman's day players were often given more than one on each tour and many have wound up at auction, although not for so much money. England caps have sold less well. The cap that Hollies wore at the Oval in 1948 failed to reach its reserve price of £12,000 in 2006. A cap belonging to Douglas Jardine, the England captain during the Bodyline series in 1932-33, was bought for £9,600 in 2003.

David Frith, a cricket historian, collector and friend of Bradman, said: “The bizarre prices paid for cricketana - most markedly for anything associated with Bradman - stem from the conviction that it's bound to be a good investment. Nobody seems to believe the Bradman legend will ever fade.

“There's often a sense of showing-off in the auction room. How overpowering is owning an item of clothing once worn by the famous? But everything, surely, has a top price. Is the 1948 Bradman cap about to become the first significant example of a cricket 'banker' going bust?”

Bidding for immortality

- In 2005 a ball used during the Bodyline series in 1932-33 was bought for £10,000. It was signed by Douglas Jardine and Harold Larwood, respectively the England captain and fast bowler.

- A pocket diary kept by Victor Trumper, the Australia batsman, during his tour to England in 1902 was sold in 1997 for £14,000.

- The bat used by Bradman on his debut Test in 1928 sold for about £65,000 in September. Bradman made 18 and one with it, then was dropped for the only time in his career.

- A complete set of Wisden Cricketers' Almanacks from 1864, the first issue, to 1999 was bought for £120,000 last year.

- Mahendra Singh Dhoni, the India captain, was bought for about £975,000 in the Indian Premier League (IPL) auction of players in February. The money that Bradman's cap could fetch this month would have been more than enough to have bought Shane Warne, the former Australia leg spinner, in the IPL auction.