The families of the four soldiers who died in Deepcut were left "deflated and disappointed" by the Blake review's conclusions, according to one of their lawyers.
By Paul Wood
BBC defence correspondent
The Blake report on the Deepcut deaths was a year in the making
Mr Blake's long awaited report - more than a year in the making - found no evidence of murder and no need for a public inquiry.
By one count, there have now been 17 separate inquiries into the disturbing events at Deepcut. There has even been a police investigation of the police investigation.
But none of these has been a full public inquiry, that is, with evidence taken under oath and in open hearings. The Deepcut relatives say they will fight on to achieve this.
They compare themselves to the Marchioness relatives, who waited 10 years to get their hearing.
By contrast, the government will now be hoping that Mr Blakes's headline recommendation - that there should be no public inquiry - will put an end to the anguished debate over Deepcut.
However, at the end of his news conference, Mr Blake said a public inquiry would only be seen as unnecessary so long as the government accepted and implemented his 34 detailed recommendations.
One of the most important of these, he said, was for a new commissioner of military complaints.
This would be an armed forces ombudsman, an independent figure outside the chain of command, someone to whom young recruits being bullied could turn.
Ministers are examining calls for an ombudsman to be appointed
The Armed Forces Minister, Adam Ingram, said the government was indeed looking at how Mr Blake's findings could be implemented - but on this issue of the ombudsman, the government had yet to make up its mind.
One family member told the BBC the ombudsman was a "cop-out", an easy option the government might choose rather than go through the long and expensive process of organising a public inquiry.
But there is at least the possibility that if the government does not create this new commissioner of military complaints, the Ministry of Defence will face renewed calls for a public inquiry, perhaps with Mr Blake's support.
Although Mr Blake did not find that the four soldiers were "bullied to death" or that there was a "culture of abuse" at Deepcut, his report was still damning enough.
He catalogued "institutional failures" at Deepcut and instances where a minority of recruits did suffer from "foul abuses".
A sergeant instructor is alleged to have punched and kicked one of those who later - according to Mr Blake's account - committed suicide. The man is also accused of propositioning five young female recruits.
Another non-commissioned officer is said to have ridden his mountain bike over recruits he considered too fat. These allegations are denied.
The report says none of the deaths could have been predicted and that in three of the four cases, the deaths were self inflicted. Mr Blake did not reach a conclusion about the fourth.
The families have always feared that something very sinister was going on at Deepcut.
They refuse to believe that their children committed suicide, pointing to multiple gunshot wounds on some of the bodies.
Mr Blake said the rapid fire of the SA 80 rifle accounted for that.
But in remarks addressed directly to the families, Mr Blake said their long campaign had already improved the training regime at Deepcut and other Army barracks.
The government says it has instructed senior Army commanders to carefully read the 400-page report and to ensure that something like Deepcut can never happen again.
For the families, this is not the end of the matter, but only another step in their long campaign.