The family of Edward O'Brien said they "unreservedly condemned" the attack and have forbidden any military trappings at his funeral.
In a statement issued through a solicitor in their home town of Gorey, Co Wexford, in the Irish Republic, Edward O'Brien's family also expressed their "deep sorrow and sympathy" for those injured in the Aldwych explosion and emphasised their abhorrence of violence and terrorism. They said they wanted no paramilitary involvement "in any way, shape or form" at their son's funeral.
Miley and Margo O'Brien were reportedly devastated by the death of their son and by the shock of the discovery that he was an IRA member. Local people have insisted that the family had no connection with the republican movement.
The inquest for O'Brien, who was killed when his Semtex bomb accidentally exploded while on the way to a target in central London, will open today.
The IRA made the admission that O'Brien was one of their men in a telephone call to RTE, the Irish Republic's broadcasting network
Yesterday anti-terrorist officers were continuing to search O'Brien's house in south London. They raided the building on Tuesday and recovered enough Semtex and bomb-making equipment for about six bombs similar to Sunday's. The police are trying to trace other IRA members through documents recovered at the scene.
In Gorey, the Catholic priest Father Walter Forde blamed the IRA in London for recruiting O'Brien. "He was the last person you would expect to be associated with anything like this," he said.
"There has been a strongly expressed revulsion for the IRA godfathers who recruit impressionable young people into violent activities."
He said of the O'Briens: "They are a very good, decent local family involved in a lot of community things, and they just feel so ashamed as well as the feeling of great loss for their oldest son."
O'Brien, described in the town as "always friendly and very popular", was last seen at home over Christmas when he stayed with neighbours. He was understood to have come to Britain to find work almost two years ago. He was then thought to have spent some time in London and possibly Glasgow.
In London the funeral of the second man killed in the massive blast in Docklands, east London, was held yesterday. John Jefferies, 68, led mourners at the service at Lewisham Crematorium in south-east London for his son, John, 31.
Meanwhile, the partner of Brendan Woolhead, 33, the Irishman injured in the bus bombing - and cleared of any involvement in the attack - spoke of the trauma.
As Mr Woolhead continued to recover in St Thomas's Hospital his partner, Gillian, said: "He can remember hardly anything about what happened - he can't remember getting on the bus that was blown up."
She told Irish radio that Mr Woolhead flew to London from his home in Dublin last Saturday to start work as a telephone engineer. She added: "I am just thinking of the future. It's infuriating - will Brendan ever be employed again with this tag that has been given to him?"
The three other people seriously injured in blast are also improving. Bob Newitt, the driver of the bus, has been taken off his intensive-care ventilator.
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