In a separate court case, Barker was also given a life sentence for raping a two-year-old girl.
It emerged Owen, who was jailed for three years, has changed his name to avoid being connected to the killing of Peter.
General secretary of the POA Brian Caton said: "The Prison Service has to make the risk assessment.
"They can take the cheap option and segregate them - but then we still need staff to monitor them 24 hours a day to make sure they do not harm themselves.
"Or we have to post extra staff to be with them when they move, when they exercise, when they go on visits, when they take part in rehabilitation - that is a huge cost.
"You have to also remember that if they are attacked, the prison officer guarding them is also likely to be assaulted."
By Mark Easton, Home editor
We have a justice system in this country that says we must name the guilty. But there's a contradiction here because we also want it to protect the innocent.
The difficulty with this case was that there was a very clear contradiction - there were other children involved who were still alive and there is a significant risk.
Some believe that in identifying those responsible for the Baby Peter case that we risk identifying those children and making their lives more difficult.
However, the judge finally decided that their identities are available to those who want to know them and have been for many months on the internet.
I think that if there is a lesson to be drawn from this in terms of identification, it's how can we better ensure that we have a proper criminal justice system that does punish those responsible for crimes but also protects other children.
The notoriety of the Baby Peter case is such that all three convicted people are likely to be given new identities upon release to protect them from vigilante attacks, according to the probation union Napo.
Assistant general secretary Harry Fletcher said: "The question will be, how well known are they in five years' time?
"And will Baby P still resonate with the public in terms of horrendous crime?
"If it does - and I suspect it will - the probation service and police will have no choice but to put in place a protection plan."
A Ministry of Justice spokesperson said: "A change of identity facilitated by government agencies is extremely rare and granted only when the police assess that there is clear and credible evidence of a sustained threat to the offender's life on release into the community.
"Even when such an assessment is made a change of identity would not be granted if it increased the risk of harm which the offender presented to others.
"The details of any new identity would be passed to those responsible for supervising offenders on release from custody."
Liberal Democrat MP for Hornsey and Wood Green, Lynne Featherstone, said she believed there would be widespread public anger if Connelly and Barker were given police protection after their release from prison.
"There's certainly a section of the public that think that they should be in jail for life and if they come out they should not receive any protection at taxpayers' expense whatsoever."
It has also been revealed that the brothers were charged with assaulting their own grandmother, Hilda Barker, who lived in Whitstable, Kent, in 1995, in an attempt to make her change her will.
That case was dropped when Mrs Barker, 82, died before giving evidence, but she told police she had been locked in a wardrobe by the pair.
It can also be reported that Baby Peter, whose surname was Connelly, had four siblings.
A judge had ordered none of the defendants could be named because those children were still being placed with alternative carers. Barker's trial for rape also contributed to the delay in naming the defendants.
Hilda Barker's former neighbour David Cole on Steven Barker and Jason Owen: 'They used to wear Halloween masks to frighten her'
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