Reverend Jackson said Britain should say sorry
Such a move would show commitment to "evening the playing field," he said.
Reverend Jackson's comments come after controversy over UK opposition to the drafting of an apology for the trans-Atlantic slave trade at a United Nations conference on racism in the South African city of Durban.
Britain prefers instead the idea of an expression of regret.
Responsibility
The prime minister's spokesman said: "The government is following an agreed European Union position which was agreed at a meeting of the general affairs council in July.
"We do not believe it is appropriate or sensible for governments today to accept responsibility for the actions of governments centuries ago.
"The important thing is what we are doing in the present."
Among its EU partners the UK's view has sympathy from Spain, Portugal and the Netherlands.
But Belgium, which holds the EU presidency, wants to move closer to African and black American demands for an apology.
The onetime US presidential hopeful insisted that slavery could not be dismissed "as if it never happened".
Subsidy
"In many ways Africa subsidised America and Europe's development," he told the BBC programme.
"If you don't feel apologetic for slavery, if you don't feel apologetic for colonialism, if you feel proud of it then say that.
"But if one has a sincere desire to overcome the ravages of the past it doesn't take much to apologise and move towards some plan for restoration."
Labour MP Kevin McNamara said he regretted the UK's position on not making an apology, although he expressed frustration that the issue had dominated the conference in Durban which he is attending as part of the European delegation.
He said that it was also unwise of the UK and the US not to send senior government ministers to the conference.
According to Mr McNamara, it sent out the wrong message that the two nations regarded the issues of slavery and Zionism, which also featured at the conference, of "not being worthy of the attention of senior cabinet members".