Andy Burnham has warned of the dangers of open-water swimming as he called the deaths of a mother, father and their teenage daughter who got into difficulty in water off Sussex “a terrible family tragedy”.

The prime minister expressed his sympathies to their loved ones as a young girl from the same family remained in a critical condition in hospital.

There was a huge emergency service response to the incident in Shoreham-by-Sea on Tuesday afternoon, when police were told four people had got into difficulty in the water.

Sussex police said it believed all four entered the water to swim. Ch Supt James Collis of Sussex police confirmed that a man, a woman and a teenage girl had died at the scene. A younger girl from the same family was taken to hospital in a critical condition, Collis added.

Officers have not named the victims but said their next of kin had been informed and were being supported by specialist officers.

Asked if the government needed to do more to tackle water safety, Burnham said: “Always. It’s so sad to hear what happened yesterday, and obviously we think there’s a young girl still in the hospital fighting for her life, and we send our best wishes and love to wider friends and family. But a real tragedy, a real terrible family tragedy.”

Speaking on a visit to north-east England, Burnham added: “Always, there’s more that can be done. Obviously, we will look in detail at what happened.

“The thing I can say today, and there is still, I think, a further heatwave to come in this summer period, it is just to remind people about the dangers of open-water swimming. The coldness, even when it feels hot outside, it can shock people, and that can cause the difficulties. So people just need to remember that at all times.”

Two air ambulance helicopters and a critical care team were sent to the scene and Shoreham RNLI said its lifeboat had been called out at 3pm.

Burnham paid tribute to those who tried to save the family. “I do need to praise the emergency services, who I know were on scene very quickly yesterday. They’ve had a busy summer, but they were there, and we thank them. As I say, just huge sympathy to the friends and the family,” he said.

There have been a series of water-related deaths in a summer of record-breaking heat. On Saturday, a 12-year-old boy drowned in the River Lea, near the Hackney Marshes, in north-east London.

In April, a woman and her young child died after getting into difficulty in the water in west London. Both died at the scene in Elthorne Park, Ealing, the Met police said. There have been at least 35 drowning deaths, including eight in July, according to a study by the London School of Hygiene & Tropical Medicine.

Joss Loader, the chair of Shoreham Beach Residents’ Association, said: “There’s just a really strong sense of shock, obviously people are really concerned for the young girl.

“A small, tightly knit community with a very deep sense of shock and that sense of disbelief you get after a tragedy because it has come out of nowhere.”

Shoreham beach is a spit of land with water on three sides from the River Adur, the estuary and the sea, and Loader said she understood the “tragic events” happened in the estuary.

“It’s school holidays and we have had a wonderful summer so the beaches have been packed with families,” she said.

“People swim from those beaches even in the winter, generally it is considered as safe as the sea can be. You wouldn’t be swimming there and think you were taking a risk.”

Anna Peacock, 81, who lives near Kingston beach across the water from Shoreham fort, said emergency services were on the scene very quickly.

“People come down to swim, particularly in the summertime and I don’t think they realise there’s a riptide along here,” she said.

“It’s very inviting to come to the sea, but the tide could carry you out in seconds, and I don’t think people have realised that.”