The cases emerged in an investigation by the Tele into ambulance response times across the two regions.

This follows concerns about a period of “unusually high demand” in Dundee earlier this month that saw one chronically ill pensioner wait six hours for attention.

Dr Jean Turner, chief executive of the Scotland Patients Association, said there needed to be a “huge debate” about the service, particularly in more rural areas.

Our investigation found wide variations in Scottish Ambulance Service (SAS) average response times.

In Tayside, ambulances responded to the most life-threatening, category A calls in an average 9 minutes 4 seconds, and urgent category B calls in 11 minutes 2 seconds.

The fastest average response (7 minutes 1 second) was in Monifieth and the slowest (10 minutes 27 seconds) in Pitlochry.

In Fife, average response times were quicker, with figures of 7 minutes 42 seconds for Category A and 9 minutes 50 seconds for category B.

A SAS spokesman said, “We continue to work hard at improving response times in Tayside and Fife.

“Last year ambulance crews had to contend with some challenging weather conditions, which impact on response times and create surges in demand.

“We are continuing to develop new ways of working in order to improve response times, particularly in rural areas.”

In Tayside, the slowest response time to a category A call was 63 minutes 27 seconds, while in Fife the slowest was 46 minutes 11 seconds.

The service provided only limited details of these incidents.

“The slowest responses in Fife and Tayside are very much exceptions and the patients’ outcomes were not adversely affected,” the spokesman said.

“The slowest response in Fife to a category A call was as a result of a surge in demand for local resources, at a time of bad weather.

“On arrival at the scene of the incident the patient declined to go to hospital for further treatment.

“The slowest response in Tayside to a category A call occurred in rural Angus as a result of the combination of distance and insufficient details provided for the patient’s location.”

The Government has set targets for the SAS of responding to 75% of category A calls within eight minutes, and 95% of Category B calls within 19 minutes.

Dr Turner said she was aware of cases in which the first response from the ambulance had been technicians, who had then had to wait for the arrival of a paramedic.

“It’s not just about the response time, it’s also about the quality of the response and the outcome,” she said.

Non-emergency calls have to be responded to within four hours, but recently a Dundee pensioner waited in agony with a broken leg for six.

Her family described the incident as a “complete disgrace”, while the SAS blamed a surge of emergency calls related to fans celebrating Dundee United’s cup victory.