The girl, thought to be around six years old, got into difficulty in the water at Hillsborough Leisure Centre yesterday afternoon.
Eyewitnesses claimed the youngster was in the wave pool section of the pool when she started struggling.
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Lifeguards performed CPR at the poolside until paramedics arrived to take over and transport the youngster to hospital.
The girl was said to have been awake and breathing when she was taken to hospital.
Steve Culf, general manager of Hillsborough Leisure Centre, praised his staff for their lifesaving actions, but some families in the water at the time said they were concerned at how the incident was dealt with.
They have posted comments on the leisure centre’s Facebook page, with one woman claiming her mother-in-law had to provide advice on how to perform CPR.
She said her sons and their friends shouted to a lifeguard that a child was ‘floating’ but their cries for help were ignored.
The woman, who is calling for an official investigation into the incident, said a lifeguard did jump to the water fully clothed but it was the girl’s dad who carried her lifeless body out of the water.
Another witness, Jackie Smith, claimed the staff on duty did not have a ‘calm command’ of the situation, which she described as ‘very scary’.
But leisure centre manager, Mr Culf, said: “We can confirm that there was an incident in our leisure pool on Sunday, where a girl was taken to hospital after getting into difficulties.
“Preventing situations such as this taking place is an essential part of our health and safety procedures and lifeguards’ training. As such, we are reviewing how the girl came to be separated from her parents and had got into difficulty.
“In a busy leisure centre such as Hillsborough, there will be occasions when our lifeguards are called into action.
“Our team are regularly trained to deal with such incidents and I am pleased with how they responded.
“CPR was administered to the girl by our team correctly before being passed to the care of paramedics who arrived quickly once the alarm had been raised.
“Our priority on these occasions is focused entirely on the person undergoing treatment.
“It is a very pressurised environment and, while we appreciate the concern of other pool users, we do use verbal instructions to try to keep the area clear so our lifeguards and paramedics can do their job. We appreciate our customers’ assistance and understanding at these crucial moments.”
Hollie Garforth, who was swimming with her daughter when the incident occurred, praised the lifeguards for their efforts to save the young girl.
She said: “From what we saw the staff saved the little girl’s life. The first few minutes after an accident like that are crucial, it’s the first aiders and first responders who actually save lives more than the paramedics/ ambulance crew do as the first aiders are the first to administer CPR.
“There were an awful lot of general public staring and standing in the way. The pool was full of kids throwing themselves all over, which must make the life guards’ job so hard to spot anyone in danger. “There were an awful lot of kids in the pool without their parents, with no supervision. Unless you are a trained first aider or are familiar with first response it’s easy to misunderstand these situations.”
Claire Dickson also praised the lifeguards.
“The little girl was given CPR and brought back to life under the pressure of members of the public getting in the way and trying to see what was happening.
“Credit to the lifeguards for dealing with this really well and saving a life.”