The East of England Ambulance Service said it was 'under extreme pressure' after crews arrived three hours and 45 minutes after her initial call.
Bosses at East of England Ambulance Service Trust have apologised to her family over the wait.
They said couldn't send an ambulance to her because due to "extremely high demand" on the service and delays at accident and emergency units.
Deputy Chief Executive Sandy Brown said: "Our sincere condolences and apologies go out to the patient's family and friends and we are truly sorry for the ambulance wait that occurred at this incident.
"Regarding this incident, we received a call just before 8pm on 2nd January to a report of a woman with chest pain in Clacton.
"Due to extremely high demand on the service and delays at accident and emergency units, we were not able to immediately dispatch an ambulance.
"A clinician in one of our control rooms made a welfare call and spoke to the patient at 9.47pm and an ambulance crew arrived at the address at 11.46pm. The patient was found unconscious and not breathing and sadly died at the scene."
He added: "We have very publicly expressed how stretched the ambulance service is and the pressures our staff and the NHS as a whole have been under the past few days.
"We are working in partnership but we are facing hospital handover delays, which can prevent us from responding as quickly as we need to.
"As a Trust, we have experienced our busiest days ever and we know our partners in the hospitals are in the same situation.
"We had more than 4,200 calls across the East of England that day, more than 1,300 of which were in Essex and more than 250 were in North East Essex."
Former health minister Norman Lamb responded to the death on Tuesday urging the prime minister not to 'stand by and allow the NHS to deteriorate'.
GMB regional officer Dave Powell said: "I'm sure this case is much more widespread than the public is aware of.
"My concern is now that we are actually suffering deaths whilst people wait for ambulances.
'On arrival, the crew had sufficient concerns to force entry to the property as the control room could not contact the patient via telephone.
'Unfortunately, the patient was found deceased in the property and there was nothing the crew could do for her.'
A statement by the ambulance service on Tuesday said the service received more than 4,100 calls on December 31 and around 4,800 on January 1.
'To put this into content, the trust's average daily volume of calls is about 3,000 calls a day,' it added.
Matt Broad, deputy director of service delivery, added: 'The trust, as well as the wider NHS, is still experiencing incredibly high demand and is under extreme pressure.'
The ambulance service previously said it has had to rely on taxis to take patients to hospital after struggling to cope with a surge in demand over the holiday period.
The MP for North Norfolk constituency, which is served by the ambulance service, said: 'Paramedics are having to work long shifts because of insufficient workforce.
'These are the human consequences of the financial state the NHS is in. This is why it's vital the government acts, the prime minister can't stand by and allow the NHS to deteriorate.
'I've been making clear that the state that the system is in, it's inevitable that people will lose their lives and failures of care will mean people will be left with long-term disabilities.
"One of the major strains is the ambulance service and its link with A&E, problems with handovers and ambulances stacking up, which leads to delays.'
Michael Le Cornu, chairman of the Tendring Pensioners' Action Group in Essex, said he was disgusted that the woman had been left to die on her own.
He said: "It's terrible that she was left waiting for such a long time. It really is disgusting.
"We have been worried about this sort of thing happening for some time and have heard similar examples, including in which a 94-year-old died.
"We are disgusted with the complacent attitude of this particular Government. Until just recently they thought there were no problems with the NHS."
