"I extended my personal condolences to King Charles but also the condolences of the Australian people," the prime minister said from London on Sunday morning Australian time.

"He's very conscious of the connection that was there between his mother, Her Majesty, and Australia.

"But he also has, of course, a close personal connection, spending six months of his schooling in Australia and we had a quite a considerable engagement and discussion."

Mr Albanese said protocol required that he not discuss too much detail of the Buckingham Palace chat but that it was "a very warm engagement".

Mr Albanese has also held informal talks with UK Prime Minister Liz Truss at her residence in Kent, their second face-to-face but the first since her move to Downing Street.

He and partner Jodie Haydon attended the Lying-In-State of Queen Elizabeth at Westminster on Saturday and then Lancaster House to sign the condolence book and make a statement in memory of Queen Elizabeth.

Mr Albanese will also address a commemorative luncheon at Australia House that will include the nine Australians who have travelled with him and Governor-General David Hurley to London at the Palace's request.

The prime minister is expected to deliver a tribute lauding Queen Elizabeth as someone who transcended barriers while maintaining a special bond with Australia.

"Even as history continued to shape us, and the bond between our two nations evolved, the affection and respect in which we held Her Majesty remained - unchanged, undiminished," he is expected to say.

"The Queen transcended barriers. You could be a republican, and still feel nothing but regard for her."

Mr Albanese will also recall the Queen's 16 visits to Australia, including a day at the races with former prime minister Bob Hawke in 1988, which he described as "one of the most Australian experiences of all".

"She celebrated our good times, and stood with us in our times of trial, bringing sympathy and comfort when it was so badly needed," he will say.

The prime minister has also revealed details of Australia's national memorial service on Thursday, following his return.

The event will be MCed by television personality Melissa Doyle, with singer Anthony Callea to perform and each of the state premiers and chief ministers, state governors, federal members, senators and opposition leader Peter Dutton to attend.

The day has been declared a public holiday.

Meanwhile, Mr Albanese says the Queen's funeral will be a "sombre day".

It will be televised at 8pm (AEST) on Monday.

Australian Associated Press