Both men were convicted of causing the explosion outside Harrods in January 1993 in which four people were injured, and a blast on a Network SouthEast train the following month, which led to massive damage. They were also found guilty of possessing Semtex and other explosives, and firearms.
Hayes was also convicted of plotting to cause explosions at Canary Wharf, Tottenham Court Road and Woodside Park tube station, all in London, in 1992.
They were caught after being filmed by a security camera as they planted the Harrods bomb, and linked conclusively by a mass of scientific evidence to the other crimes.
Pleas of not guilty to all charges had been entered after the pair refused to answer the counts against them. The judge told them: 'It is only by the greatest good fortune no lives were lost.'
Hayes told the court he had nothing to say in mitigation: 'I am proud of everything I have done,' he announced to the stunned court.
Hayes and Taylor were like no IRA terrorists the police had come across. Intelligence and detective work had failed to pick up any trace of them as suspects.
They had been missed because the authorities were looking for Irishmen. But the two had no known connection with Ireland - there was not even a trace of an attachment to the country through holidays and there are still huge gaps in detectives' knowledge of the bombers' lives. Neither made any statements after their arrests.
Police sources say they have no idea how or when either made the transition from being 'weekend Socialist Workers' in the 1970s to working for the IRA in the 1990s.
In Hayes's flat, police found literature associated with Red Action - a splinter of the Socialist Workers' Party, founded in 1981 - and a copy of the Irish Republican News, as well as anti-fascist material. Red Action has been vocal in its support of the republican movement, but these were clues, not explanations.
The police have been aware since the 1980s that IRA recruits for mainland campaigns in Britain are no longer exclusively young, working-class Catholics from Northern Ireland.
More recently, recruits have been middle-class, or from southern Ireland, or even only Irish by descent. But the common assumption underlying all investigations had been that the IRA would not take two unknown Englishmen into their confidence to this extent.
That appears, however, to be what happened, perhaps over a period of 10 years of testing and proving themselves in tasks such as hiding a gun or delivering a vehicle.
Hayes, 41, born in Willesden, north-west London, was divorced in 1988, and neither his former wife nor his sons - aged 19, 18 and 12 - had anything relevant to tell the police. He has a degree in business studies from what was then Central London Polytechnic, and worked since 1983 as a computer programmer, most recently for Daiwa, a Japanese company in east London.
He was made redundant in September 1992, just before the bombing campaign began. None of his colleagues had anything useful to tell the police.
Taylor had worked since 1989 as a shelf-stacker at nights at the Tesco store in Bethnal Green, east London. Between 1961 and 1973 he had served in the British Army as a radio operator with the Royal Signals Corps, but never in Northern Ireland. At his flat, the police later found a United Nations peace medal he had been awarded after one tour of duty. On it he had written 'IRA'.
Nor do they know how Hayes and Taylor worked with the IRA. Warnings for all the bombings gave the IRA codeword and were in an Irish accent. The 'bomb factories' at Hayes's flat and lock-up garage appeared to be bankrolled by the IRA - there was what appeared to be an account book for items such as vans, which were always paid for with cash.
Detectives also found a list of targets - public buildings, senior soldiers and politicians - which suggested that Hayes at least had built a position of trust. But they are still unsure how many other gang members got away.
Some of the men buying vans and cars used in the bombings had very different descriptions from Hayes or Taylor. An Irishman, Patrick Kelly, 41, was jailed for 25 years last year for driving a Volvo lorry containing a massive bomb, which was stopped by police in Stoke Newington, north London, in November 1992, just before the Canary Wharf bomb. Although he was tried separately, that lorry has since been linked by scientific evidence to the Hayes bomb factory.
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