At a Bolton inquest into their deaths a coroner said the accident was "unimaginable and unexpected" and was one of the worst tragedies he had come across.
Mr Wallwork, who was originally from Swinton in Salford, was married to his second wife Susan for six years before the tragedy unfolded in Co. Sligo, Ireland, in December 2011.
The family moved there about six or seven years ago, after Mr Wallwork divorced his first wife Donna Farrimond, the children's mother, who is disabled and lives in Wigan.
Chief Fire Officer for Sligo Paul Coyle said an investigation of the property discovered a blockage close to the top of the chimney.
He told the court through a statement that he concluded a "coincidental and incredible" set of circumstances were responsible for the deaths.
The amount of carbon monoxide in the room would have risen quickly to "very dangerous" levels as the family sat there unaware.
The bodies of Mr Wallwork and his children were found the next day when his step-daughter, Vicky, arrived after failing to get any response by phone.
After repeatedly banging on doors and windows of the bungalow in Gurteen, she saw Mr Wallwork unresponsive in an armchair with the children on the floor and the television and Christmas lights still on.
Mrs Wallwork, who was in hospital being treated for cancer at the time, died about six months later. Pathologist Dr Michael Curtis said the cause of all three deaths was carbon monoxide poisoning with high levels detected in the blood.
Coroner Alan Walsh recorded verdicts of accidental death and added: "I have found it to be one of the most tragic cases I have heard in the court after sitting here for 12 years."
After the hearing, Mr Wallwork's brother-in-law Arthur Flather said: "Trevor was a devoted dad, brother, son and uncle.
"He was much-loved and the children were gorgeous and their teachers both in Ireland and England said how well-behaved they were. As a family we want to encourage people to fit carbon monoxide poisoning detectors."
- The Daily Mail
