Thousands of children were relocated to Australia and parts of the British Empire up to 1974.
Many experienced "unacceptable depravity", the first hearing in the independent inquiry into child sexual abuse in England and Wales has heard.
One migrant, David Hill, called for perpetrators to be "named and shamed".
Meanwhile the Independent Inquiry into Child Sexual Abuse (IICSA) has apologised and referred itself to the information commissioner after mistakenly sending out confidential information relating to abuse victims.
Mr Hill was 12 when he was sent with his two brothers to the Fairbridge Farm School in Western Australia.
He told the hearing: "We'll never be able to undo the great wrong that was done to these children.
"But what is important to the survivors of sexual abuse is where this inquiry is satisfied with the evidence - name the villains.
"Many of them are beyond the grave and therefore beyond the law.
"But it would bring a great deal of the comfort to the people who as children were victims of these people if they were named and shamed."
Inquiry counsel Henrietta Hill QC said claims of "systematic sexual abuse" in institutions and work environments would be heard throughout the inquiry.
The children, she said, were sent without consent of parents, wrongly told they were orphans, and denied basic details about their family backgrounds during their future lives.
For the government, Samantha Leek QC said: "Child migration is wrong. It should not have been sanctioned or facilitated...
"The lifelong consequences for those involved are a matter of deep and sincere regret."
In 2009, the Australian government apologised for the cruelty shown to the child migrants.
Britain also made an apology in 2010. The apology contained no specific mention of sexual abuse.
The abuse scandal of the British children sent abroad
By BBC home affairs correspondent Tom Symonds
One of the many criticisms levelled at the Independent Inquiry Into Child Sexual abuse centre on the view that it is too focused on the past.
This investigation dates back to 1945, but some of the child migrants are still alive, and their mistreatment as children is undeniable.
Perhaps, then, this is safe ground for a public inquiry hoping to demonstrate its value following two and a half years of controversy.
The hearings may well be able to establish the wider pattern of sexual abuse, which permeated the institutions abroad which received children.
This has never been attempted by a previous official investigation.
The inquiry panel will also be able to draw conclusions from the sheer length of time it has taken for some of those abused to disclose what happened, something that is likely to be a common theme in the inquiry's work.
However, on a day when this troubled project really started to be making progress, it managed to shoot itself in the foot by leaking sensitive data - not for the first time.
The first phase of the Independent Inquiry into Child Sexual Abuse (IICSA) inquiry is looking at the way organisations have protected children outside the UK.
Between 7,000 and 10,000 children were moved to Australia after World War Two.
They were recruited by religious institutions from both the Anglican and Catholic churches, or charities, including Barnardo's and the Fairbridge Society, with the aim of giving them a better life.
Many, however, went on to suffer physical and sexual abuse in homes and so-called farm schools run by religious orders and charities.
Aswini Weereratne QC, representing the Child Migrants Trust (CMT) support organisation, said this "long overdue inquiry" would hear of a "crushing catalogue of sexual abuse, deprivation, violence and abuse".
Ms Weereratne said the inquiry will hear from 22 former child migrants - their average age was nine when deported and one was aged only three or four years old.
The abuse that some of the children sent abroad were said to have suffered included "torture, rape and slavery", Ms Weereratne said.
Speaking on behalf of former child migrant Oliver Cosgrove, who was sent to Australia in 1941, Imran Khan said: "(It was) a scheme to populate the empire with good, white British stock and which led to the physical, emotional and sexual abuse of countless children, many thousands of miles away from their families."
A Â£6m family restoration fund was set up to allow the migrants to travel to the UK and ministers are now considering extending it.
The independent inquiry was set up after the death of DJ Jimmy Savile in 2011 when hundreds of people came forward to say he had abused them as children.
The IICSA has apologised after mistakenly sending out confidential information.
People who had registered an interest in attending victims' forums - which are being organised by the inquiry - were sent an email on Monday that revealed the email addresses of others who had registered.
The BBC understands that 90 people were affected.
Nigel O'Mara, an abuse survivor and core participant in the inquiry, told the BBC that "this breach of data is very concerning to survivors as these are the very people we are supposed to trust with the details of our abuse".
The hearings are taking place at the International Dispute Resolution Centre in central London, with the first phase concerning Australia expected to last 10 days.
A former child migrant has called for an inquiry to "name the villains" responsible for the sexual abuse of British children sent overseas.