The King and Queen have sent their “very best wishes” to King Frederik X and Queen Mary of Denmark on the day of their accession to the throne.

Charles wrote a message, shared by Buckingham Palace, in which he also paid tribute to “the many years of service” of Frederik’s mother, and Europe’s longest-reigning monarch, Queen Margrethe II.

She announced her abdication in a televised New Year address after telling how back surgery she underwent last year led to “thoughts about the future”.

Buckingham Palace said Charles has written privately to the 83-year-old, who stepped down on Sunday after a 52-year reign.

Queen Margrethe signed her formal abdication at a meeting with the Danish government at Christiansborg Palace, in Copenhagen, making way for Frederik, 55, and his Australian-born wife Mary, 51, who is the daughter of Scottish immigrants.

In his letter to Frederik and Mary, Charles wrote: “My wife joins me in writing to convey our very best wishes on the day of your accession to the throne of the Kingdom of Denmark.

“I look forward to working with you on ensuring that the enduring bond between our countries, and our families, remains strong, and to working together with you on issues which matter so much for our countries and the wider world.

“I pay tribute to the many years of service of your mother, Her Majesty Queen Margrethe II, and remember fondly the frequent visits between our countries, including our visit to Copenhagen and Elsinore in 2012.

“I was delighted that Your Majesties were able to attend our coronation last year and I much look forward to future opportunities to celebrate the close connection that unites our countries and our families.”