A United Nations judge says the UK is likely to owe more than £18tn in reparations for its historic role in transatlantic slave trade.

A report co-authored by the judge, Patrick Robinson, says the UK should pay $24tn (£18.8tn) for its slavery involvement in 14 different countries.

According to Robinson, the sum was an “underestimation” of the damage caused by the slave trade and he was amazed some countries responsible for slavery think they can “bury their heads in the sand”.

“Once a state has committed a wrongful act, it’s obliged to pay reparations,” said Mr Robinson, who presided over the trial of Slobodan Milosevic, the former Yugoslav president.

Mr Robinson has been a member of the International Court of Justice (ICJ) since 2015 and has been researching reparations as part of his honorary presidency of the American Society of International Law.

He brought together a group of economists, lawyers and historians to produce the Brattle Group Report on Reparations for Transatlantic Chattel Slavery.

In total, the reparations to be paid by 31 former slaveholding states – including Spain, the United States and France – amount to $107.8tn (£87.1tn), the report calculates.

The valuation is based on an assessment of five harms caused by slavery and the wealth accumulated by countries involved in the trade. The report sets out decades-long payment plans but says it is up to governments to negotiate what sums are paid and how.

In his speech at the London mayor’s office, Robinson said reparations were “necessary for the completion of emancipation”.

He said the “high figures” in the Brattle Report “constitute a clear, unvarnished statement of the grossness” of slavery.

In his own speech, London Mayor Sadiq Khan said the transatlantic slave trade “remains the most degrading and prolonged act of human exploitation ever committed”.

“There should be no doubt or denial of the scale of Britain’s involvement in this depraved experiment,” Mr Khan said.

Caribbean and even African countries have sought slavery reparations from western governments for years with limited success.

“For me, it goes beyond what the government and the political parties want. Khan added

“Of course they should set the tone. But I would like to see the people of the United Kingdom involved in this exercise as a whole.”

When asked if the £18.8tn figure could be too little, Mr Robinson said: “You need to bear in mind that these high figures, as high as they appear to be, reflect an underestimation of the reality of the damage caused by transatlantic chattel slavery. That’s a comment that cannot be ignored.”

He said the sums in the report “accurately reflect the enormity of the damage cause by slavery”.

It amazes me that countries could think, in this day and age, when the consequences of that practice are clear for everyone to see, that they can bury their heads in the sand, and it doesn’t concern them. It’s as though they are in a kind of la la land.” he said