The poet Helen Dunmore is in the running to become the second posthumous winner of the Costa book of the year award for her final collection, Inside the Wave – which was written in the last weeks of her life – triumphing in the poetry category of the annual literary prize.

Expressly rewarding enjoyability, the Costa book awards are open only to writers in the UK and Ireland. There are five categories – novel, first novel, biography, poetry and children’s book – with the winner of each then vying for the overall £30,000 book of the year prize. If she wins this, Dunmore will be the second writer to take the top gong posthumously in the prize’s 46-year history, after fellow poet Ted Hughes won for Birthday Letters in 1998.

Dunmore, who died in June 2017 aged 64, wrote 10 poetry collections and 12 novels. Inside the Wave considers her terminal cancer diagnosis and impending death. It includes the poem Hold out your arms, written 10 days before she died. In it she imagines death as a mother: “You push back my hair / – Which could do with a comb / But never mind – / You murmur / ‘We’re nearly there.’” The judges called the collection “a final, great achievement”.

Her son Patrick Charnley said the family was thrilled by her win, and added: “I know she would be, too.”

“Poetry was at the heart of all of mum’s work, so we’re delighted,” he said. “Inside the Wave deals extremely bravely and frankly with death. In the 11 months we knew my mother was going to die, she shared a number of these poems with us, so it is very personal to us. What is shown by this fantastic win is how people who didn’t know her have also connected to it”

Poetry category judge Moniza Alvi said the decision to award the prize to Dunmore was an easy one. “These are poems that can connect us with each other, at a deeper level,” she said. “It is not an austere book. The truths are sharp and they’re not comfortable, yet they are also life-affirming and beautiful.”

Author Gail Honeyman. Photograph: Philippa Gedge/HarperCollins Publishers

The current favourite to win the overall book of the year award, according to bookmakers William Hill, is Scottish author Gail Honeyman, who took the first novel award with Eleanor Oliphant Is Completely Fine. Following the lonely life of a survivor of a childhood trauma, the book has been widely acclaimed and has also been optioned by Reese Witherspoon’s production company, Hello Sunshine. “This is a narrative full of quiet warmth and deep and unspoken sadness,” wrote Jenny Colgan in her review for the Guardian. “It makes you want to throw a party and invite everyone you know and give them a hug, even that person at work everyone thinks is a bit weird.”

Man Booker longlisted author Jon McGregor won the Costa novel award for Reservoir 13, a “hypnotic, compelling and original” novel according to the judges, about the search for a missing girl in the Peak District. McGregor told the Guardian in November that he was excited to be nominated for a Costa award and the Goldsmiths prize for experimental fiction: “It felt like a very experimental book while I was writing it, but it’s not necessarily that experimental on the surface, although it demands quite a lot of the reader … a certain patience.”

In the biography category, historian Rebecca Stott scooped the award for In the Days of Rain, her memoir about growing up in the Exclusive Brethren, a fundamentalist Christian sect. In the children’s book category, bestselling author Katherine Rundell won for The Explorer, an adventure story of four children fighting to survive in the Amazon rainforest.

Each of the winning authors, selected from 620 entries, will receive £5,000. The book of the year will be chosen by category judges Moniza Alvi, Simon Garfield, Freya North, Sophie Raworth and Piers Torday, as well as British Vogue editor Laura Bailey, presenter Fern Britton and actor Art Malik. The winner will be announced on 30 January.

For fans of Dunmore, the good news doesn’t stop with Inside the Wave: a new collection of unpublished short stories titled Girl, Balancing, will be published in June. “She said we may wish to publish a collection of short stories and pointed me to some she had not published,” her son Patrick Charnley said. “People responded time and time again to her work, and I think they were sad to think they wouldn’t get any more. So we’re very pleased to be able to share this with people.”

2017 Costa book awards winners

Novel: Reservoir 13 by Jon McGregor (4th Estate)

First novel: Eleanor Oliphant Is Completely Fine by Gail Honeyman (HarperCollins)

Biography: In the Days of Rain by Rebecca Stott (4th Estate)

Poetry: Inside the Wave by Helen Dunmore (Bloodaxe Books)

Children’s book: The Explorers by Katherine Rundell (Bloomsbury Children’s Books)