Six-month-old Chevaz Palmer was rushed to hospital on 9 April suffering from mild dehydration.
But despite a warning call from her GP, doctors at University College Hospital failed to see her. Five and half hours after admission she was dead.
According to the Patient's Charter, children should be seen within 30 minutes.
Prim and Michael Palmer (right) had hoped an inquest would highlight what went wrong. But the St Pancras coroner, Dr Douglas Chambers, is refusing to hear the the case.
'He has made it quite clear in a letter to us that there is no need for an inquest as it is a natural death,' said Mr Palmer.
Dr Chambers admitted on a recent BBC2 documentary, Taking Liberties, that he took a tough line on holding inquests and that he has had more judicial reviews against him than any other coroner.
The Palmers, from Islington, north London, have been refused legal aid, but plan to take the matter to the High Court to get an order for an inquest to be held.
Detectives at Holborn have launched an investigation after a formal complaint by the family. The hospital has also started an internal investigation after admitting there were delays.
Mr Palmer said: 'I feel the hospital's lack of efficiency contributed to my daughter's death. The Palmers allege it was one and a half hours before Chevaz was seen by a doctor, and a further one and a half hours before a bed was found and their baby received treatment.
The couple also claim that nurses struggled to get a drip operating and that batteries on one piece of equipment were flat.
Mr Palmer said: 'I am angry and scared that a hospital can behave in such a way. There didn't seem to be any urgency.
'They were warned by the GP that she was coming in and she should have had a doctor to meet her. She was suffering from gastroenteritis but she shouldn't have died. She needed fluids and she wasn't given them quickly enough.
'Chevaz was shaking and struggling for breath while nurses stood around discussing bets on a horse race. They didn't they realise she was sick.
'We kept complaining because she was shaking violently and they just told us it was because she was breathing fast. Then a nurse asked us if we thought she was in pain. She was groaning and writhing about the bed in agony.
'Why wasn't she taken into intensive care? My daughter is no longer with us and I think the delays are a major factor.
Sam Ryall, a hospital spokesman, insisted there had been no faulty equipment and staff had acted according to normal procedures. 'We are taking this very seriously. An inquiry is under way, headed by the paediatric and emergency services manager.
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