London — The brother of the late Princess Diana claims in his upcoming book that King Charles III, then Prince Charles, "sounded giddily elated — like a lottery winner," right after his ex-wife died in a Paris car crash in 1997. 

It is the latest bombshell allegation to emerge from "Swan Song: Diana, My Sister," the book by Charles Spencer, Diana's younger brother, set to hit shelves next week.

In an interview airing this weekend on "CBS Sunday Morning," Spencer explains his explosive allegation that a year after the royal couple's divorce, and with the nation in mourning just after Diana's death at the age of just 36, Charles seemed upbeat.

"Obviously I'm not justifying or criticizing," he told CBS News. "I'm just reporting that's the fact."

Spencer said he believed the then-Prince of Wales' attitude could have been due to him finally feeling free to pursue Camilla, who he later married, and who is now known as Queen Camilla.

"I said in the book that that might have been it, yeah," he told CBS News.

Princess Diana's brother claims Prince Charles seemed "upbeat" after she died 00:36

Buckingham Palace pushed back earlier this week after the first allegation from Spencer's book emerged: a claim that Charles had told him days before Diana's funeral that "we'll forget her soon enough."  

In a statement unusual in its force for the staid institution, the palace said that while the monarch wouldn't comment directly on a book, he "is mindful that the pain of fraternal grief can cloud reason, affect judgement and colour memory, even many years after such a loss." 

CBS News royal contributor Royya Nikkhah said Thursday that the royal family was in for "a very tricky few days," predicting that Spencer's claims about what the king said after Diana died would be "just the beginning of a serialization that will go on … and we know there are going to be some pretty sensational claims." 

"They will have to decide whether or not they're going about each and every claim, or just to make that first response we've heard from the palace their definitive response," said Nikkhah, who is the royal editor for The Sunday Times newspaper. "But it's going to put them into fight mode, and it's going to be very difficult for the king."

Spencer also claims Charles told Diana he didn't love her before their fairy-tale wedding in 1981, and that Diana contemplated suicide more than once.

There has been no further response from Buckingham Palace to the latest claims from Spencer's book, excerpts of which are being published by the Daily Mail tabloid in Britain. 

The allegations from Charles Spencer are damaging for King Charles and the royal family, but speaking to people outside Buckingham Palace on Friday morning, CBS News found many who were sympathetic to the monarch.

"I love the king, and I love the royal family," said one man. 

A young man, walking with his mother, was less adamant, saying he wasn't "big on the king anyway," but adding that the entire episode, to him, seemed "a shame."

"I'm probably the other way," said his mother. "I probably think it's totally unnecessary and it is just a story at the end of the day. And people are going to believe what they want to believe. But I don't know why it has to keep getting dragged up to be honest."

With five days to go until Spencer's book is available, and more excerpts likely to be published in the interim, it is virtually guaranteed to be dragged up again, and soon.

Tucker Reals contributed to this report.

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