Chile's president is to visit the British Museum and Churchill War Rooms in London, on the second day of his visit to the UK.
The main business of Sebastian Pinera's trip will take place on Monday, when he meets the Queen and David Cameron.
Mr Pinera, whose country is still celebrating the rescue of 33 trapped miners, told reporters: "It started as a tragedy and it ended as a blessing."
He brought fragments of rock from the San Jose mine as gifts for his hosts.
"I asked the miners to bring one rock each so I can give it to the Queen and to David Cameron," Mr Pinera, who arrived in the UK on Saturday before a European tour, told the BBC.
He also brought a copy of the first message that the miners sent to the surface after what he called 17 "anguished" days of searching.
The rescue of the miners after 69 days has made headlines worldwide.
Thirty-one of the miners have now been released from hospital, with the remaining two being transferred to other hospitals.
One is suffering from a dental infection and the second is suffering from vertigo symptoms.
Speaking after landing at Heathrow on Saturday, Mr Pinera described how the rescuers refused to give up the search.
"We committed ourselves to do whatever was necessary to save their lives," he said.
"We had a commitment that we would search for the miners as if they were our sons. It started as a tragedy and it ended as a blessing."
Inspired by Churchill
Shortly after he landed at London's Heathrow Airport on Saturday, and as he prepared to meet members of the UK's Chilean community, he paid tribute to his homeland.
Mr Pinera said his country had shown the world "a good example of the real meaning of commitment, courage, faith hope and unity."
He said: "We did it because we were united, we did it because we were convinced, and did it because we would never leave anyone behind. And that's a very good principle for Chile and for the world."
Earlier the 60-year-old said Winston Churchill's "blood, toil, tears and sweat" speech had provided inspiration to him during the battle to save the miners.
Fittingly, he was visiting Churchill's War Rooms in London on Sunday.
Mr Pinera also said he ignored political advice to steer clear of the rescue effort.
"Many people thought the rescue was impossible and advised me not to get involved, to keep my distance," he said.
"I decided to take full responsibility without any political consideration.... We made a commitment to look for the miners as if they were our sons."
Like Mr Cameron, Mr Pinera was only elected this year, and his visit to London is thought to have been planned many months ago.
He is thought to be hoping to persuade more British companies, including mining corporations, to invest in Chile.
After sightseeing in London on Sunday, he will meet Mr Cameron and have an audience with the Queen on Monday, who has extended an invitation at the last minute following the mine rescue.
On Saturday, Mr Pinera, who greeted the miners with a hug after their rescue, said he was looking forward to both meetings.
He said: "We have a great admiration for David Cameron. He is a very good friend of ours. He was able to create a new majority to transform and modernise the Conservative Party and to find new solutions for old problems and that's something that I'm sure will be very good for England."
He said he had also bought them a copy of the first message the miners had sent to the surface after they were trapped. It read: "We are well in the shelter, the 33".
He continued: "And also we are bringing the gratitude of all the Chileans because we received a lot of help from our friends around the world."
The Harvard-educated politician said lessons had to be learned from what had happened with the mine.
He said: "One of the lessons is that we have to be much more careful and committed with the safety, lives, the health of our workers."
He is visiting France and Germany later this week.
Mr Pinera had earlier revealed that his father-in-law died only hours before the miners were rescued and he had told the president: "Don't give up. Keep working to rescue the miners."