The UK has signed up to “structured, time-bound, inclusive and good-faith” talks that address the “historical harms” of the transatlantic slave trade, Commonwealth leaders in Antigua have said.

The formal conclusions marking the end of the Commonwealth Heads of Government Meeting, known as the communique, is the joint text setting out what has been agreed.

The 18 page document, external includes a paragraph in which the leaders “welcome the agreement of the Government of the United Kingdom to engage in a structured, time-bound, inclusive and good-faith dialogue with affected parties addressing the transatlantic trafficking of enslaved Africans and its historical harms”.

It comes after Prime Minister Andy Burnham opened the door to a formal apology on behalf of the UK for its role in the slave trade, while ruling out the prospect of reparations.

Officials said the timeframe for the talks would be agreed at a later date, though the Foreign Secretary Ed Miliband has suggested they are likely to conclude in around a year.

Asked whether the government might reach the point of a formal apology by the time it hosts the G20 leaders’ summit in Manchester next November, Miliband told BBC Newscast, external: “Broadly speaking, yes.”

The rationale among British diplomats in committing to the wording in the communique is to try to offer reassurance that there is a sense of urgency to deal with the issue, even if a date for doing so is not yet confirmed.

This will be determined, sources said, in the “structured dialogue” the UK is promising with countries that have long demanded that the pain and lasting legacies of the slave trade are, as they see it, properly addressed.

Burnham said his “new approach with the Commonwealth” had been “well received” at the summit.

He said it had “been the most successful meeting of the Commonwealth in recent times,” adding that “the King’s words have resonated powerfully here and we’re really pleased with how it’s gone”.

King Charles III, speaking in his role as Head of the Commonwealth, told the meeting: “The transatlantic trade in enslaved persons still casts a shadow over these islands and other Members of our Commonwealth.

“As I have said before, that shameful chapter of history is one that fills my heart with horror and my soul with the most profound personal sorrow.”