For a medical emergency, you must always call 999. Community First Responders (CFRs) are volunteers mobilised by the ambulance service via 999 calls, so you cannot contact them directly in an emergency.
South Hams Hospital
The South Hams has one hospital, South Hams Hospital in Kingsbridge, which is not an accident and emergency department but provides urgent care services. For actual A&E, you would need to travel to a hospital with a full accident and emergency department, such as Derriford Hospital in Plymouth, which is the nearest major hospital.
Chillington Health Centre will see holidaymakers who require urgent medical attention. However, the surgery's official advice is to contact your own home GP practice first. Your registered GP has access to all your medical records and can often provide phone, video, or online consultations, which may resolve the issue without needing an in-person visit in Chillington.