"The slave trade ended; slavery did not end and the legacy has not ended," Rev Jackson told Christian Today after a meeting with black church leaders on Monday.
Rev Jackson is in the UK this week as part of a visit organised by Churches Together in Britain and Ireland to highlight racial justice.
"The legacy of slavery lingers in ways that can be measured today," he said, pointing to the higher mortality rates and shorter life expectancy within black communities, as well as high numbers of young black people in prison and substantial disparity between black and white students at top universities such as Oxford and Cambridge.
"Hard work and effort and excellence cannot offset the impact of inheritance and access, so there you have structural inequality," he said.
Rev Jackson made clear, however, that an apology from the UK Government for the slave trade would be "empty without a commitment to reconstruction".
"Words and action must go together, otherwise apologising is a ceremony," he said.
Rev Jackson went on to criticise the church for its complicity in the slave trade.
"The church for too long offered moral justification for our [black people's] slavery and apartheid. The church made the case to give tyrants and oppressors a comfort zone without a commitment to social change," the civil rights campaigner asserted.
