The book, Servants of the People, by political commentator Andrew Rawnsley, suggests that the prime minister and his chancellor frequently engage in battles over who has the greatest authority.
However a Downing Street spokeswoman has dismissed the book, saying that it was sensationalist and that key elements were "100% wrong".
The Treasury called it "malicious and baseless gossip".
'Psychological flaws'
Among the allegations contained in the publication is that Mr Brown wanted to sack the Governor of the Bank of England, Eddie George in 1997, because he saw him as a threat.
The book alleges that Mr Blair had to telephone Mr George personally to make sure he stayed in place.
The prime minister is said to have often become infuriated with his chancellor.
In another potentially damaging disclosure, Mr Rawnsley's book suggests that Mr Brown is unimpressed by Mr Blair's economic abilities.
The book also deals with the infamous occasion on which sources apparently close to Mr Blair allegedly said that Mr Brown had "psychological flaws".
The author claimed the comment was made by someone "with an extremely good claim to know the mind of the prime minister".
'Total nonsense'
A Downing Street spokeswoman said: "As far as we are concerned, books like this aren't written to sell copies, but to sell serialisation rights for large sums of money, which requires the author to say something sensationalist, guaranteed to send the Westminster media village into one of its periodic lathers.
"No prime minister and chancellor in history have ever worked so closely together.
"We don't intend to waste much time on this book," she said, adding that key elements were "100% wrong".
A Treasury source said: "The Treasury is not going to comment on malicious and baseless gossip with no foundation in fact whatsoever."
A Bank of England spokesman dismissed the claims about Mr Brown wanting to sack Mr George as "total nonsense."
He stressed that Mr Blair never got in touch with Mr George, and also pointed out that the governor is appointed for a fixed five-year term, during which he is all but impossible to dismiss.