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1 June 2015 Last updated at 22:46 BST
Notorious crime boss, Reggie Kray, penned the 215 exchanges to Carol Clerk, the ghost writer of his autobiography, while serving a life sentence in prison.
Victoria Irvine, a valuer at McTear's Auctioneers, told BBC Scotland the letters were "fascinating pieces of crime memorabilia".

The excluded New York Times said the move was "an unmistakable insult to democratic ideals".
The bar came hours after President Donald Trump delivered another attack on the media, saying that "fake news" was the "enemy of the people".
The BBC has asked the White House to clarify its exclusion.
BBC bureau chief in Washington, Paul Danahar, said: "We understand that there may be occasions when, due to space or circumstances, the White House restricts press events to the established pool. However, what happened today did not fit into that pattern."
He added: "Our reporting will remain fair and impartial, regardless."
Friday's briefing had been scheduled as an on-camera event in the briefing room but was changed to an informal off-camera event, known as a "gaggle", in Mr Spicer's office.
Explaining the move to go off-camera, he said: "We don't generally do, we haven't done briefings when the president's had a major event."
Mr Spicer said an "expanded" pool of journalists had been invited to the gaggle. Pools are not uncommon - the journalists attending then share their reporting with the White House press corps.
However, the choice of those attending, including groups seen as friendly to the Trump administration, and the fact that other journalists who asked to attend were refused entry drew condemnation from media groups.
White House Correspondents' Association President Jeff Mason said it was "protesting strongly".
The BBC, CNN, the New York Times, the Guardian, the Los Angeles Times, Buzzfeed, the Daily Mail and Politico were among those excluded.
Those allowed into the room included ABC, Fox News, Breitbart News, Reuters and the Washington Times.
The Associated Press, USA Today and Time magazine refused to attend as a protest against the move.
Both the Washington Post and McClatchy said they were unaware of the exclusions at the time and that had they known, their reporters would not have attended the gaggle.
Both said they would not participate in future briefings if the exclusions continued.
An anchor for Fox News, seen as supportive of the Trump presidency, also revealed opposition to the move.
Bret Baier tweeted: "We joined w/all networks in a complaint to WH about the incident."
When asked at the gaggle, Mr Spicer denied CNN and the New York Times had been denied access because the White House was unhappy with their coverage.
But he said: "We are just not going to sit back and let false narratives, false stories, inaccurate facts get out there."
CNN anchor Jake Tapper said the exclusion was "not acceptable, in fact it's petulant. And indicative of a lack of basic understanding of how an adult White House functions".
Washington Post executive editor Marty Baron said the White House move was "appalling".
In an editorial, the LA Times said: "If the intent was to intimidate reporters into writing fewer things that the administration does not like, and more things that it does, it is doomed to failure."
The New York Times editorial said: "That First Amendment can be inconvenient for anyone longing for power without scrutiny. Mr. Trump might want to brush up on what it means, and get used to it."
Hours before the briefing, Mr Trump had delivered a strong attack on what he called "fake news" in the media, targeting stories with unnamed sources.
He told the Conservative Political Action Conference (CPAC) that reporters "shouldn't be allowed to use sources unless they use somebody's name. Let their name be put out there".
He said "fake news" was the "enemy of the people".
Reports claiming his campaign aides had contact with Russian intelligence officials have particularly irked the president.
A collection of letters described as being "historically important", which were written by one of the UK's most notorious gangsters, are to go under the hammer in Glasgow.
[NEXT_CONCEPT]
Media groups have reacted angrily after several, including the BBC, were barred from an informal briefing with White House Press Secretary Sean Spicer.