Testimony from a Ukrainian lawyer, Sergei Karpenko, claimed Mr Kolomoisky threatened him at a meeting in 2003.
Four days later Mr Karpenko's assistant was badly beaten in the street and the following month Mr Karpenko himself was attacked with an iron bar and repeatedly stabbed, the court heard.
Mr Pinchuk's lawyers said the gangsters who carried out the attack were linked to Sergei Nikitin, who had been Mr Kolomoisky's personal bodyguard and later ran a private security company, BOG, owned by Mr Kolomoisky and the other defendant in the current case, Gennadiy Bogolyubov.
Mr Nikitin was found dead in a river in Dnipropetrovsk, central Ukraine, just weeks later on August 30, 2003, having been stabbed 10 times.
The gangster who carried out the murder was also found dead in what was initially claimed to be a suicide.
However, further examination after his body was exhumed showed he had been shot under the chin, the court heard.
"Mr Kolomoisky thinks nothing of making serious physical threats to his opponents, as well as perverting the criminal process."
Jonathan Crow QC, in an earlier hearing
Mr Kolomoisky "strenuously denies" the claims of any illegal activities.
Although Ukrainian prosecutors passed a resolution to charge him with ordering Mr Karpenko's murder in 2005 it was never proceeded with, the court heard.
Mr Pinchuk's lawyers said a Ukrainian prosecutor had "admitted in a recorded conversation" that he was promised money by Mr Kolomoisky in exchange for shutting down the investigation of his alleged role in the murder plot, although he was in fact never paid.
They also argued the series of allegations about Mr Kolomoisky were relevant to the current dispute over ownership of an iron ore mining company, KZhRK.
"Mr Kolomoisky thinks nothing of making serious physical threats to his opponents, as well as perverting the criminal process,"Jonathan Crow QC, for Mr Pinchuk, said at last month's hearing.
"These are hardly the actions of a man who would hand over the management of KZhRK to Mr Pinchuk because he was afraid of Mr Pinchuk's ability to stir up false allegations."
Laurence Rabinowitz QC, for Mr Kolomoisky, said: "The allegations are hotly contested and are of the most serious nature conceivable, including ... allegations that [Mr Kolomoisky] conspired to commit murder."
Mr Justice Males in the High Court ruled that evidence about the "Karpenko episode" will not be allowed in the full trial, which was due to begin on Monday.
The case - in which legal fees alone are likely to exceed £50 million - demonstrates how English law courts have become highly popular in the international business world for the resolution of disputes.
It comes after another so-called mega-case in which Boris Berezovsky, an oligarch who had fallen out with the Kremlin in the Nineties, sued Roman Abramovich, the Chelsea Football Club owner, seeking £3 billion in damages.
Berezovsky was humiliated in court, lost the case and was found hanged at his home in Berkshire in March 2013.
The latest High Court cast a spotlight on what Mr Justice Males described as the "rough and tumble" world of Ukrainian business dealings at the time.
Mr Pinchuk, 54, made his fortune through a series of deals, many of them struck when his father-in-law, Leonid Kuchma, was president of Ukraine.
Mr Pinchuk began a relationship with Mr Kuchma’s glamorous daughter, Elena — 10 years his junior — in 1997 and married her in 2002.
His connections have led the defendants in the case to claim he was able to exert political influence in the country and potentially secure "trumped up charges" against them, the court heard.
Mr and Mrs Pinchuk have worked hard to build their reputation on the world stage, spending large sums on philanthropy but also on one of London’s finest houses - bought for a record £80 million in 2008 - and an expensive art collection, including several works by Damien Hirst.
"To spend money is much more exciting than to make it,” Mr Pinchuk once said.
His opponents — Mr Kolomoisky and Mr Bogolyubov, both 52 — are estimated to be richer than their rival, and are more discreet.
Mr Kolomoisky lives in Switzerland, and Mr Bogolyubov lives in Belgravia, central London.
Both men, with a net wealth of about £5 billion, have given large amounts to charities.
The central issue of the current case was Mr Pinchuk's claim that he brokered a deal with his former business partners to buy KZhRK, a former Soviet nationalised industry, on his behalf but the two men did not deliver on the agreement.
Mr Pinchuk has been seeking up to $2 billion in damages plus his original £90 million investment.
Lawyers for Mr Kolomoisky have previously said Mr Pinchuk's claim "lacks all credibility".
They also told the court last month that Mr Pinchuk's lawyers had made a "startling admission" in previous legal documents that he had hired private investigators to follow Mr Kolomoisky.
Details of the settlement were not made available.
