The sovereign wrote: “I wanted you to know how deeply shocked and saddened both my wife and I are to hear of the many people who have lost their loved ones as a consequence of the recent, tragic incident in Itaewon, Seoul.
“However inadequate this may be under such heartbreaking circumstances, we extend our deepest possible sympathy to all the bereaved families.
“We also offer our special thoughts and wishes for a speedy recovery to all those who suffered injury.
“Recalling our meeting during your own gracious visit to London to attend the funeral of Her late Majesty The Queen, please be assured that the United Kingdom stands in solidarity with the people of the Republic of Korea at such a time of national mourning.”
Mr Yoon was one of the several heads of state to have travelled to England ahead of September 19 to attend the state funeral of the 96-year-old monarch.
Other leaders included US President Joe Biden, French President Emmanuel Macron and New Zealand’s Prime Minister Jacinda Ardern.
Members of foreign royal families were also in attendance, including Denmark’s Queen Margrethe II and Spain’s King Felipe.
King Charles’s message came one day after the Prince and Princess of Wales, Prince William and Kate, issued a brief message of support to South Korea via their Twitter account, KensingtonRoyal.