The ambulance trust serving the region is investigating eight "serious incidents" in March.
They involve delays in getting patients to hospital, including four cases in which people died.
The East of England Ambulance Service (EEAS) admitted the service had fallen short, and said it was investing in extra staff and ambulances.
"And we're talking about time-critical patients, not someone who has just cut a finger.
"It's happened to me with a patient who was having severe breathing difficulties. I had to wait for an ambulance to come from 50 miles away. Regrettably she passed away before the ambulance arrived."
The EEAS covers Essex, Hertfordshire, Bedfordshire, Cambridgeshire, Norfolk and Suffolk, a population of almost six million people.
The service needs to find savings of almost £60m in the five-year period to 2016-17.
But paramedics say the funding crisis has been compounded by previous management putting too much of its resources into lone-response paramedics at the expense of fully staffed ambulances.James Sadler was left stranded twice after suffering first a heart attack and then, a month later, chest pains at his home in Sheringham, Norfolk.
On the first occasion, the sole paramedic who attended was told that one ambulance had been diverted to another emergency and a second had run out of petrol. The third ambulance to arrive got him to Norfolk and Norwich Hospital three hours after his family had made the 999 call.
As he waited to get to hospital, his heart stopped beating.
"I cheated death twice, first at home and then in the ambulance. The paramedic was superb, but the delay was disgusting. The problem is not getting into hospital," he said.On the second occasion, a paramedic again responded quickly to a call from his family, but the ambulance arrived late and then broke down at his house. Eventually he got to hospital several hours after the 999 call was made.
Although the trust recorded eight serious incidents linked to delays in March, the problem has been developing since the end of 2011.
Figures released after a Freedom of Information request show that incidents where patients waited for more than 30 minutes after the first responder called for back-up increased from 1,241 in December 2011 to 2,884 last November. The biggest problems were in Essex.
The investigation into the serious incidents will determine if the delays played a part in any of the four subsequent deaths.
A new chief executive, Andrew Morgan, has been brought in to sort out the problems facing the trust. In a report last month, he said senior managers had taken their eye off the ball as they pursued foundation trust status.
Mr Morgan said there had been a lack of "clear and visible leadership from the board".
The trust says it is "seeking to recruit" an additional 351 frontline staff, and is investing an additional £5m in its frontline operations, as part of a plan to improve the service. An extra 25 fully crewed NHS ambulances will also be deployed in areas where delays have been most acute.
"We have to improve our service to better support patients and staff. A number of patients have waited too long for an ambulance and in some areas there has been an overreliance on rapid-response vehicles.
"Our turnaround plan sets out how we will achieve that. The changes we require will not happen overnight, but we are starting to see some improvements in our services," said Mr Morgan.