The ambulance service said that on Friday crews were hit by delays at both the Princess Royal and Royal Shrewsbury Hospitals, which meant the equivalent of seven ambulances were out of service for an entire shift.
Firefighters were scrambled from Church Stretton to Carding Mill Valley on Friday evening after the woman's husband was advised by the National Trust to call the fire service.
A West Midlands Ambulance Service spokesman said it apologised to the patient for the delayed response in reaching them.
"It is standard practice that the fire service would assist in the rescue of a patient from a hillside," said the spokesperson. "However, we would like to apologise to the patient for the delayed response in reaching them to provide medical assistance.
“Sadly, we have seen some patients wait a very long time for ambulances to arrive as a result of long hospital handover delays. The pressures in health and social care meant that when our crews arrived at A&E they were unable to hand over patients to hospital staff and therefore couldn’t respond to the next patient in the community."
But they said that there has been a marked improvement since the turn of the year.
The spokesperson added: "There has been a significant improvement since the turn of the year with delays reduced at hospitals across the region, but where delays happen, it does have a significant impact on the ambulance service, as happened on the day in question.
"We continue to work with our partners to find new ways to reduce the delays even further, so that our crews can respond more quickly and save more lives.”
A spokesman for Church Stretton Fire Station said: "Church Stretton firefighters are at another rescue up the Carding Mill Valley.
"This time a lady has fallen on the hillside with a suspected broken ankle.
"Her husband rang for an ambulance but they were all tied up and could be a seven hour wait time.
"The Carding Mill Valley and the Long Mynd National Trust recommended calling the local fire service for assistance."
The spokesperson added that on arrival they managed to immobilise the lady and safely carry her down on a stretcher.
"Due to the time wait the lady was taken to A&E by car for further investigation," they added. A family member took the woman to hospital.
"Doing a good deed like this makes us all feel good inside and everything worthwhile," added the fire crew.
Shropshire Fire & Rescue Service scrambled one fire appliance including the Incident Support Unit.
A spokesperson said one person was rescued from a steep embankment with an injured lower leg.
Sheila Fryer, acting deputy chief operating officer for The Shrewsbury and Telford Hospital NHS Trust (SaTH), said: “We are sorry that patients faced long waiting times in our emergency departments (EDs), but we would like to reassure patients that emergency and urgent care was prioritised.
"The combined impact of the longest period of junior doctors’ industrial action, so far, from July 13 to 18, followed closely by consultants’ industrial action on July 20 and 21 resulted in long waits in EDs and consequently ambulance handover delays.
“Our hospitals remain under pressure and all available additional space within the trust is open. We are working hard with system partners to release additional capacity in the community to support patients who are ready to be discharged from hospital as quickly as possible to free up beds and improve flow through our EDs.”