The hospital believed Thomas Rogers was not at risk
His family say it then took the hospital 36 hours for the to let them know he had died alone.
Health officials at Whipps Cross University Hospital, Leytonstone, East London, have ordered an investigation into how Thomas Rogers died.
But the family are demanding a public inquiry.
Mr Rogers, 74, needed treatment for burns after he collapsed unconscious against a radiator at his sheltered accommodation home in Woodford Green, Essex.
His condition was assessed by a triage nurse who decided Mr Rogers was a medium priority patient when he arrived at the department.
"It is not acceptable that he was left for nine hours without seeing a doctor."
Mr Rogers's condition was checked "fairly regularly" by nursing staff, who decided he remained "stable".
But when a nurse went to check at 0210BST on 14 August he was found collapsed in a cubicle and pronounced dead 10 minutes later, despite the efforts of an emergency resuscitation team.
Public inquiry
Mr Coles said the hospital had apologised to Mr Roger's family and that they would be investigating the circumstances of his death.
"We are all very sorry about what happened to Mr Rogers. We are introducing a full investigation. It is not right that situation was allowed to happen," he told the BBC.
Mr Rogers, a widower who was born in Gateshead, Tyneside, but moved to Essex 25 years ago to work as an engineer at the Dagenham Ford plant, had three sons, Les, Alan and David.
They have now called for a public inquiry to be held into their father's death as they believe that he might have survived if he had been seen earlier.
Alan said: "He died without anybody being there, no family what so ever. He died alone in hospital."
Les, 49, of Fenham, Newcastle, agreed: "How could this happen? What other case was more serious than my dying father?
'Natural causes'
"We don't believe anyone has gone out there to kill him, and we are sure they are hard-working people, but it is a terrible thing that has happened.
"There's no way he should be dead. He should be here with us.
"We are asking for an open inquiry, not a behind-the-doors hospital inquiry, and we believe the findings should be made public and it should take actions to make sure it doesn't happen again."
A spokesman for the Walthamstow coroner said a post mortem examination showed Mr Rogers had died of an aneurysm, which was classed as natural causes and no inquest would be held.
A Department of Health spokesman said: "We are very concerned at the accounts of this gentleman's treatment.
"We understand he was seen three times by nurses, but not by a doctor in the assessment cubicle.
"We want to see the results of the investigation as soon as possible and have asked that the family see those results."