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But, campaigners said his statement does not go far enough and have called for a full disclosure of facts and compensation for the families of African people who were sold for slavery.
Mr Blair's comments stop short of a formal apology but are intended to end a long controversy among some black activists before the 200th anniversary next year of Britain's ban on slave trading.
Writing in New Nation, a black community newspaper that has pressed for several years for an apology for slavery, Mr Blair will emphasise that his view is a personal one, although similar remarks will be made in a written statement to Parliament. He will say: "It is hard to believe that what would now be a crime against humanity was legal at the time.
"Personally I believe the bicentenary offers us a chance not just to say how profoundly shameful the slave trade was, how we condemn its existence utterly and praise those who fought for its abolition, but also to express our deep sorrow that it ever happened, that it ever could have happened and to rejoice at the different and better times we live in today."
Speaking on the BBC's Today programme Esther Stanford of the campaign group Rendezvous of Victory said: "This statement does not go far enough. To repair the harm we are talking about educational reparations, financial reparations, family and cultural reparations.
"If we don't deal with this now it's tantamount to saying that you can commit crimes against humanity."
Ms Stanford said she agreed "most definitely" with calls for legal compensation. However, she said that did not include seeking redress from the families of African leaders who were involved in organising the slave trade.
"You don't indict a whole country of Africa for the excesses of a few people who were forced to partake," she said.
"No-one blames Jewish collaborators for their part in the Holocaust."
No 10 declined to say whether Mr Blair's intervention was intended as a statement of regret or form of apology, saying only that Mr Blair's words spoke for themselves. The Prime Minister has also given instructions for Britain to co-sponsor a resolution at the United Nations put forward by Caribbean countries next year.
David Lammy, Culture Minister, also speaking on Today, defended the Prime Minister saying that he did not want to get into a "blame fest" over whether compensation should be made available.
"Tony Blair's statement is first a political statement. It's one that follows along on a long tradition. Tony Blair has gone further than any other leader in the West and has struck the right balance. I think it is the right tone and its right that we move forward together," he said.
"I think the business of compensation is not really productive. I don't want to get into a blame fest. I want dialogue and progress."
Next year's anniversary commemorates the Abolition of the Slave Trade Act, passed in 1807 after it was blocked for two years by the Lords, which made it unlawful for any British subject to capture and transport slaves. It introduced fines for British captains of £100 for every slave on board their ship.
The legislation paved the way for the better known Abolition of Slavery Act in 1833 that gave all slaves in the British Empire their freedom and paid compensation to slave owners.
Mr Blair's statement is the product of lengthy discussions within the Government in which the key figures were Baroness Amos, Britain's first black woman Cabinet minister, and John Prescott, whose Hull constituency was represented by William Wilberforce, a leading campaigner against slavery.
Mr Prescott has chaired an advisory committee since the beginning of the year comprising anti-slavery groups, churches and others. Lady Amos, a member of the committee, was photographed leaving Downing Street this month clutching papers on which her personal notes about Mr Blair's planned statement were visible. These indicated that Mr Blair was "prepared to go further than being asked to".
There had been concern within the Government that the 200th anniversary of the abolition of the slave trade might become dominated by debate on demands for an apology and even for reparation to be paid.
Instead, ministers hope that the events in March, including a service at Westminster Abbey, will have focus on the moral lead given by Britain.
Michael Eboda, editor of New Nation, welcomed Mr Blair's remarks. He said: "It's pretty much as close to an apology as he can give taking into account the advice he has been getting from the Foreign Office in terms of the threat of legal action. I am pleased with it."
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