A coastguard search for two men who went missing in the sea off Devon during a Christmas Day swim has been called off.

Emergency services were called to Budleigh Salterton at 10.25am on Christmas Day after concerns were raised for people in the water.

A number of people were safely brought to shore but two men – one in his 40s and another in his 60s – could not be found. Of the people who were rescued, two were checked by paramedics and one was taken by ambulance to hospital as a precaution.

The coastguard stopped searching the water at 5pm but police said onshore inquiries continued into the evening. The men’s families have been informed.

While there is no official weather warning in place on Boxing Day, some sea swims have been cancelled and police in Devon and Cornwall have urged people not to get into the water.

On Christmas Day, Det Supt Hayley Costar, of Devon and Cornwall police, said officers had responded to “a truly tragic incident” in Budleigh Salterton. “Our thoughts remain firmly with the families and friends of the two men who are currently missing and to all who may have witnessed and be impacted by the incident,” she said.

“There have been weather warnings in place this week and a number of official and unofficial swims have already been cancelled. While there are no official warnings in place for tomorrow, we urge anyone with plans to go swimming in the sea on Boxing Day not to.”

The coastguard said its search was stood down at 5pm. A spokesperson said: “Alerted at around 10am, Exmouth and Beer coastguard rescue teams, RNLI lifeboats from Exmouth, Teignmouth and Torbay, coastguard search and rescue helicopters and fixed-wing aircraft were sent to the scene to assist, alongside police and ambulance service.

“Searches have continued throughout the day to find two men believed to still be in the water. After extensive shoreline and offshore searches, the coastguard part of the search was stood down at 5pm.”

Julia Robb, a resident who had been watching swimmers at the beach before the men went missing, said it had been a “very cold and windy” day and the waves “would have been at least 6ft”. She said it was only when she heard helicopters it became clear something was wrong.

Robb added: “It was a sad thing to happen on what had been such a positive morning. I just feel sorry for those who have been affected. I think it will be shocking for the whole community. We are a small town. People are very friendly. I think it is important to think of the friends and families of those who have been affected.”