The three-year-old son of a British scientist may have permanent brain damage after he and his mother were attacked by a giraffe, his family said on Thursday night.

Finn Williams and his mother Katy, 35, are fighting for their lives following the attack at the South African nature reserve where they live.

Mrs Williams was waiting outside with son Finn for her husband Sam to arrive home when they startled the animal and its young calf.

Conservation biologist Dr Williams arrived while the female giraffe was still attacking them and chased it off.

Mother and son were airlifted to hospital from the Blyde Wildlife Estate, an upmarket gated reserve with 154 homes protected by electric fencing and security guards.

Both had operations, with doctors working to release pressure on Finn’s brain. His US-born mother suffered multiple injuries.

Both were in a critical but stable condition at a hospital in Johannesburg on Thursday.

Sam Williams’ aunt, Anne Oliver, revealed Finn may have been left with permanent brain damage. "We understand that Finn had an operation to remove a blood clot on the brain. We’ve been told that he will have brain damage," she said.

"The last we heard was that Katy was having surgery and she is in an induced coma. She’s got multiple injuries."

Mrs Oliver, 61, added: "As a family, we are all very, very upset. We just feel so helpless because of how far away they are."

Dr Williams, 36, said in a statement that it was a "difficult time" but he regarded the attack on Monday as "an unfortunate act of nature where the giraffe saw his wife and son as a threat to her young one".

The academic had been on a trail run on the estate in the northern Limpopo province.

Family lawyer Marina Botha said: "Dr Sam Williams found his wife and son still under attack by the giraffe within a mere 150m of their family home, where Finn normally waits for his father to return from his run."

The 394-hectare Blyde Wildlife Estate – named after the nearby Blyde River – offers a clubhouse, gym, tennis courts and restaurant to its residents. Antelope, giraffe, wildebeest, hippopotamus and crocodile are among the species free to roam the estate.

Riaan Cilliers, the Blyde Wildlife Estate manager, said: "We are all in shock about this very sad incident and we assure the family that they are in our prayers."

Details of the attack were unclear on Thursday. Giraffes are normally docile but can use their head and neck as a club if threatened. Mrs Williams and her son may also have been trampled.

Jack Standish, Mrs Williams’ father, was last night flying from the US to South Africa. He wrote on Facebook that he felt ‘helpless’ as his ‘wonderful daughter and loving grandson’ were operated on in hospital.

According to The Times, plans are being made to move the giraffe and her young from the estate.

Dr Williams, who was born in Wakefield, West Yorkshire, has two degrees in biology from Manchester University. He received his PhD at Durham in 2012 and is now a post-doctoral research fellow at the University of Venda in Limpopo.

His wife has also carried out extensive research in animal-related fields and is in a post-doctorate position at the University of Mpumalanga.

The couple met at Durham and have lived in Africa for around ten years – the last four in South Africa, and before this Zimbabwe

Earlier this year cameraman Carlos Carvalho, 47, was killed by a giraffe that slammed its neck into him while he was filming for British TV show Wild At Heart in a South African reserve.