Prime Minister Tony Blair has expressed his "deep sorrow" over Britain's role in the slave trade.
Mr Blair said it had been "profoundly shameful", according to an article for the New Nation newspaper.The government is reportedly setting out its plans for next year's bicentenary of the abolition of the slave trade.
Esther Stanford, of the Pan African Reparation Coalition, said all countries that had ever been involved in slavery should give a full apology.
"An apology is just the start - words mean nothing," she told BBC News.
"We're talking about an apology of substance which would then be followed by various reparative measures including financial compensation."
She said: "If we do not deal with this now it is tantamount to saying that you can commit crimes against humanity, against African people and get away with it."
In February, the Church of England General Synod voted to apologise to the descendants of victims of the slave trade for profiting from the "dehumanising and shameful" slave trade, two centuries after its members helped bring about its abolition in Britain.
The General Director of the Evangelical Alliance, Rev Joel Edwards, has welcomed the Church of England's statement of apology, saying, "repentance is a good first step".
Joel Edwards, the General Director, said, "I commend the Prime Minister for his statement and his acknowledgement of the role Britain played in this inhuman trade. Of course, Britain's industrial supremacy was significantly fuelled by the slave trade and it was also the first country to outlaw this horror.
"The bi-centenary commemorations will provide all of us with an opportunity to reflect upon and remember the millions of African slaves who died, as well as to pay tribute to those courageous men and women who fought, struggled and campaigned to end the horror of the transatlantic slave trade."
