Grey re-tells the events of James's 2011 original from the perspective of its antagonist, Christian Grey.
The book, writes the Evening Standard's David Sexton, "loyally repeats every line [and] every excruciating email".
According to the Telegraph, the result is "as sexy as a misery memoir".
"How often do Ana's cheeks flush pink?" writes Bryony Gordon in her one-star review. "How many times does she make him feel ten feet tall?
"And he really should go and see someone about all that prickling his scalp does."
James's original told of the steamy relationship between Grey, a millionaire businessmen with an interest in bondage and sadism, and literature student Anastasia Steele from the latter's perspective.
According to the author, "thousands of readers" had requested to hear Christian's point of view since the book's publication.
The new book was published on 18 June, as that is the date of the character's birthday in Fifty Shades and the two sequels that followed.
Writing in The Guardian, chick-lit author Jenny Colgan described the original novel as "a rather fun and fairly mild portrait of a woman's sexual fantasy".
In her opinion, though, "it is almost impossible to read Grey and not assume the narrator is going to end up in jail".
"Instead of light-hearted and repetitive mild S&M, the 'love affair' is now the twisted work of an utter psychopath," she continues.
Yet the Daily Mirror's Francesca Cookney is more forgiving, saying fans of the Christian Grey character "will be pleased to discover he's no less complex than he seems".
The first book in James's trilogy was adapted into a film this year by director Sam Taylor-Johnson, with Jamie Dornan as Christian and Dakota Johnson as Anastasia.
Taylor-Johnson has since ruled herself out of directing the planned sequels, based on James's books Fifty Shades Darker and Fifty Shades Freed.
Critics have savaged EL James's rewrite of her erotic bestseller Fifty Shades of Grey, with one calling the writing "bad throughout" and another accusing it of "rapturous self-regard".