The King has said the slave trade “fills my heart with horror” – but stopped short of offering an apology – in a speech to Commonwealth leaders as the UK faces mounting demands to pay reparations for its role in the slave trade.

King Charles told a summit in the Caribbean: “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.”

Earlier this week prime minister Andy Burnham signalled that he was “open” to a formal apology for Britain’s role in the transatlantic slave trade and approved £40m in aid funding for the Caribbean amid calls for the UK to pay reparations.

But former Archbishop of Canterbury Justin Welby has warned that forcing millions of ordinary Britons to fund huge sums in slavery reparations would be a “moral evil”.

Writing for , he argued it would be a “vast fine on the entire British people for a crime they did not commit”.

“The vast majority of Britons have no connection to slavers’ profits – and nor did their ancestors,” he wrote.

“What about those sailors of the Royal Navy who died liberating the slaves, or the UK parliamentarians who spent their lives campaigning for the abolition of slavery and its trade? Should their descendants be treated differently?”

He added: “To do even the right thing in the wrong way makes for more evil. It is right to act differently, wrong to act foolishly.

“Investment in new technologies and solving current existential dangers in partnership will build more wealth than a futile and unjust payment of fake ‘reparations’ ever could.”

As the King delivered his keynote speech to presidents and prime ministers on Tuesday, he described his “growing commitment” to finding ways to work in “modern partnership to address the wrongs of the past with action for the future”.

He said: “And yet history also teaches us that evil need not have the last word; that character and courage can combine to overcome the most monstrous injustice, as they did with the determination to end international trade in enslaved people, in which the Royal Navy played such a leading role.

“The more I have furthered my own understanding of the issues, through listening, learning and looking, the more committed I have become to finding ways for us to work in modern partnership to address the wrongs of the past with action for the future.

“Through improving access to education, investing in jobs and opportunities, encouraging intra-Commonwealth trade, and inspiring vital climate resilience measures across the world, I have always felt that there is so much that can be done to help lift up those who struggle against hardship and disadvantage.”

At the perimeter of the Commonwealth Heads of Government Meeting (CHOGM) area was a small protest, where activists held placards that read “You say you regret so apologise”, and “Apologise for the greatest crime against humanity and let’s have reparatory justice”.

The funding announced by Mr Burnham will be given over three years to speed up critical infrastructure investment, including green energy schemes in the Caribbean, according to Downing Street.

The prime minister is expected to begin discussions with Caribbean leaders about the prospect of offering a formal apology for the UK’s role in selling enslaved people for profit. But he has ruled out offering direct financial reparations.

King Charles said in his speech: “History can be hard to compass, viewed as it is through the prism of time, which can be both clarifying and distorting, and yet its consequences resonate with contemporary force.

“Our history inspires us, can appal us, yet it can always teach us. We cannot change the actions of those who came before us. We can, however, learn from the past.”

Britain’s royal family has a long association with the transportation and selling of enslaved people for profit.

Elizabeth I backed the lucrative dealings of John Hawkins, one of Britain’s first slave traders, and Charles II encouraged the expansion of the enterprise.

The Duke of Clarence, George III’s son, later to become William IV, opposed the campaigns of slavery abolitionists.

The King also said: “All around us, trust between nations is under critical strain, as international norms and systems are tested to their limits.

“Brutal conflict stalks our world, destroying lives and casting long shadows across the globe. Technology is transforming our societies and our economies at dizzying speed, with little certainty about where it might lead us.”

The King also addressed the “catastrophic reality” of climate change, saying: “Each of these is a challenge of the highest order. Together, they comprise the crisis of our time.”