King Charles and Prime Minister Andy Burnham will arrive in Antigua for a Commonwealth leaders' summit next week to find the demand for slavery reparations written across the capital: on billboards, placards, T-shirts, in letters, and at a candlelight vigil for the thousands of Africans trafficked to Antigua and Barbuda during the transatlantic slave trade.

The message organisers promise is that reparations is not an issue the British delegation will be able to avoid. James Knight of Citizens for Reparatory Justice, which is organising some of the demonstrations, said the king and the UK government had made protest necessary. "It is definitely necessary that we make known our deep sense of indignation in response to what has been announced ahead of the meeting by the British government and King Charles that there will be no apology, no reparations," he said. Announcing that while travelling to a meeting where people have asked for the matter to be discussed was, he said, "extremely insulting [and] insensitive".

What Burnham has offered

On Friday, Burnham went further than any previous British prime minister in an article for the Guardian, writing: "We are offering a structured dialogue with those affected by the transatlantic slave trade. Listening to calls for a formal apology on behalf of the British state will form an important part of this process. I am open to them."

That is a shift in tone. It is not a shift in policy on money. The BBC reports that Burnham ruled out financial reparations, calling them "not the right answer". He described the slave trade as a "brutal and barbaric violation" and said Britain must "face up to the past", while arguing that British people today cannot be held liable for historical wrongs committed in a different age.

"I do not think that British people today can be held liable for historical wrongs, however heinous, that happened in a different age under different laws and in which they played no personal part," he wrote. A government source told the BBC that opening the door to an apology was "morally the right thing to do".

The gap between apology and money

The distinction Burnham is drawing is the one that will define the summit. An apology is a statement about the past; reparations are a transfer of resources in the present. Caribbean governments and campaigners have argued for years that the second must follow the first, and the UK government has never formally apologised for slavery or offered to pay reparations.

Burnham's "structured dialogue" is designed to keep the conversation open without committing to a figure. That may satisfy London's need to look constructive while protecting the Treasury, but it leaves the central question unanswered, and the protesters in St John's are not treating process as a substitute for substance.

Caribbean nations have renewed calls for the UK to apologise for its role in the slave trade, and for reparations, as King Charles tours the region.

Why the summit matters to London

Downing Street believes it is in the UK's interest to strengthen the Commonwealth at a moment when China and Russia are seeking to exert influence. The prime minister's calculation is that a visible, functioning summit is worth more than a fight over money.

That calculation is being tested in public. King Charles is touring the region, and the protests follow him. The symbolism of the head of state of the former colonial power arriving to discuss the future of a club that includes the descendants of the enslaved is not lost on either side.

The domestic politics

Burnham's position also reflects the politics at home. Promising an apology costs little in budgetary terms and speaks to a moral argument many voters accept. Promising money would open a debate about scale, recipients and legal liability that no UK government has wanted to start.

The phrase "structured dialogue" is doing a lot of work in that sentence. It signals willingness to listen, and it defers the question of what listening produces. For campaigners, that is the same deferral they have heard before.

What to watch

Three things will show whether the summit changes anything. First, whether the king or the prime minister uses the word "apology" in Antigua rather than in a newspaper article. Second, whether any Commonwealth government secures a commitment to a formal negotiation on reparations, even without figures. Third, whether the protests stay peaceful and small enough for the summit to proceed on its economic agenda.

For readers following the diplomacy thread, our coverage of the Canada-EU Alliance for the Future shows how another Western government is trying to build like-minded coalitions as old relationships shift, and the UK trade development plan sets out London's push for non-domestic markets. The Obama-Trump arts rally is a reminder of how quickly symbolic political disputes become campaign material.

The confirmed facts are the summit, Burnham's article, his openness to an apology, his rejection of financial reparations and the planned protests. Whether an apology is actually delivered in Antigua is not yet known.