A novel written by a prominent book industry figure in which persecuted gay man Alan Turing has sex with a woman and fathers a child has been criticised online for its portrayal of the codebreaker.

The Turing Protocol was released in July and was written by Nick Croydon, the CEO of QBD Books, the largest Australian-owned bookshop chain, where the book is being heavily promoted.

Published by Affirm Press, which was bought by Simon & Schuster last year, the novel’s cover features the question: “If you had the power to change history, would you dare?”

In the thriller, Turing, the brilliant British wartime mathematician and computer pioneer, builds a time travel machine and has sex with Joan Clarke, with whom he secretly fathers a child. Turing is otherwise depicted as gay and the story includes details of his persecution for his sexuality.

In real life, Turing was briefly engaged to Bletchley Park colleague, Clarke, when the pair were employed in vital code-breaking during the war. He was later convicted for “gross indecency” with another man and died by suicide at the age of 41 after enduring chemical castration.

Queen Elizabeth II posthumously pardoned Turing in 2013, four years after prime minister Gordon Brown apologised for his “appalling” treatment.

Croydon told The Australian newspaper he had not pretended Turing was straight, but needed to give him a child for the purpose of his plot. “I wrote this novel as a tribute to him. I wanted to highlight the genius that he was, but also the injustice that he suffered,” he said.

As of Tuesday afternoon, the book had received 115 ratings on Goodreads, with five stars making up 21% and one stars making up 64%. Many of the most positive reviews came from first-time Goodreads reviewers.

The negative reviews included anger about what some claimed was the “erasure” of gay history.

“Anyone who is aware of Alan Turing and his prosecution will be scratching their head in disbelief,” one reader wrote.

“Erasing the whole point of Alan Turing’s tragedy is one of the worst things someone can do. Erasing LGBTQ history, erasing a real person’s pain? … Turing was not some fictional character to straight-ify,” wrote another.

The book is QBD’s fiction book of the month and is being actively marketed by the company, including a promotional Channel 7 interview in which Croydon explained that his favourite subjects at school were history and mathematics.

Authors who have endorsed the book include historical fiction writer Fiona McIntosh and former QBD fiction book of the month author, Chris Hammer, who compared the book to Dan Brown’s The Da Vinci Code. Prize-winning author Trent Dalton described the book as “wildly imaginative” and urged people to “read the Turing Protocol now”, while Candice Fox said it was “vivid”.

Commenting on gay erasure broadly, Equality Australia legal director, Heather Corkhill, told Guardian Australia that “erasing or marginalising LGBTIQ+ people and characters from historical and cultural narratives to fit a more heteronormative or ‘traditional’ worldview is not a new phenomenon – but it risks erasing our shared history and diminishing our understanding of the LGBTQ+ experience”.

“At no time did I say Turing wasn’t gay,” Croydon said, according to the Australian. “The book makes it very plain that he is gay. It talks about how he had to hide the fact that he was gay, and in the historical note page at the back of the book I again acknowledge the travesty of the treatment he received.”

In a statement released last week, QBD said throughout the novel, Turing’s “identity as a gay man is neither erased, questioned nor diminished”.

“Speculative historical fiction often examines phenomena like lavender marriages – arrangements where LGBTQ+ individuals married opposite-sex partners due to societal pressures, ensuring protection and companionship – which were common during Turing’s era and beyond.

“Regarding reviews, it’s not unusual for friends, family, colleagues and peers to provide reviews of an author’s work. QBD Books staff are a team of avid readers across the country who engage with literature passionately, some of whom have shared their genuine views on the book – both complimentary and critical.

“QBD Books’ Book of the Month program follows a rigorous selection process that highlights debut or new authors who have written standout works. Each month submissions are received from publishers, and new releases are reviewed by our team of expert buyers, after which we select four titles for the whole calendar month to spotlight.”

QBD, Simon and Schuster and Croydon have been contacted for comment.