Detective Chief Inspector Mick Holland, deputy head of the investigation, told the resumed inquest on Tim Parry, 12, and Johnathan Ball, 3, that although the IRA had claimed responsibility for the attack on 20 March last year, those responsible for planting the two time-delayed bombs in litter bins had not been traced.
John Hibbert, the Cheshire coroner, recorded verdicts of unlawful killing. He said: 'It is now almost 11 months since the town of Warrington was devastated by the explosions in this busy pedestrianised shopping area on a Saturday immediately before Mothering Sunday, when whoever was responsible must have been aware of the terrible havoc they would cause and the frightful injuries and deaths which would ensue.
'No one has been charged with causing these two deaths - yet. One hopes that in due time there will be.'
He hoped that someone 'with a conscience' would come forward and give the police information.
The parents of both the boys killed in the attack, in which another 71 people were injured, were in court.
The coroner said Tim Parry, who had gone to buy a pair of Everton football shorts when he was hit by shrapnel, had died five days later from head and facial injuries without regaining consciousness. Johnathan, who died immediately, had suffered 26 different shrapnel injuries.
Det Ch Insp Holland said the first of two explosions happened in Bridge Street at 12.25pm. Two people were slightly hurt.
But immediately afterwards, people in Lower Bridge Street moved away from the scene of the first explosion into the pedestrianised area of Bridge Street while at the same time people in the town centre who had heard the explosion made their way into the same area.
Det Ch Insp Holland said that 62 seconds after the first explosion, a second device was detonated in a litter bin 75 yards away.
He said: 'The explosion inside the litter bin caused the steel bin liner to fly 10 yards away from its original location. Part of the cast-iron outer shell disintegrated and formed shrapnel projectiles. These, with the resultant blast wave, caused death and injury to people in the immediate vicinity.'
Tim Parry's father, Colin, said he was a 'little confused' about the nature of phone calls that had been received allegedly warning about the bombs.
Det Ch Insp Holland said two calls were received. One at 11.43am by the Samaritans in Manchester, where an anonymous male caller with an Irish accent said there was a bomb in the town centre.
A second call at 11.58am from a similar caller went to the Samaritans in Liverpool saying there was a bomb in Boots in the city centre.
'There was no mention of Warrington in either call and no reason to interpret that Warrington was involved.'
After the inquest, Mr Parry said he thought it was 'regrettably unlikely' that his son's killers would be caught.
'I would like to stress that it is not through any lack of police endeavours but it is such an enormous and difficult task, without inside information being passed confidentially to the police, to expect an arrest in a case like this.'