South Western Ambulance Service (SWASFT) has declared a “critical incident” because of a surge in demand over Bank Holiday weekend.
The service tweeted on Sunday that patients may face longer ambulance times due to “extreme pressures”.
It also revealed that ambulance workers dealt with almost 3,200 incidents on Saturday – the highest in 2021.
Similar numbers are expected on Sunday, the service added.
SWASFT told people to turn to alternative services if the call is not “life-threatening”.
It tweeted: “We have declared a critical incident due to extreme pressures on our service.
“As a result, some patients may wait longer for an ambulance while others could be advised to access alternative services if their call is not life-threatening.
“We need you to only call 999 in a genuine, life-threatening emergency so we can help those most in need."
It comes after the service predicted last week that it would be handling 3,000 calls a day during the bank holiday weekend.
The service said that the daily number of incidents it dealt with had risen to 2,913 in the previous week.
This was up from 2,627 before lockdown restrictions were eased on 17 May.
The Trust normally deals with around 2,650 emergency incidents a day, it added.
SWASFT said at the time that people should only call 999 for an ambulance in a medical emergency when someone is seriously ill or injured and their life is at risk.
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Those with non-life threatening but urgent problems like broken bones, sprains or burns are instead urged to contact NHS 111.
Lead paramedic Ed Hill told the BBC: "With the nice weather and people going out with friends and family, we are asking the public to help us and that they are only calling 999 for genuine life-threatening emergencies.
"We are trying to save 999 ambulances for those that need us the most."
He also advised people to take pain relief medication or a first aid kit with them when heading out.
A South Western Ambulance Service NHS Foundation Trust spokesperson said: “If you have a non-life-threatening but urgent medical problem, please call NHS 111 who can advise you on the most appropriate place for care and also call an ambulance if necessary.
“Our hardworking ambulance crews, control room staff and volunteers will continue to prioritise anyone who is critically ill and ask that you help us help you by only calling 999 in a life threatening emergency.”
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