Fourteen-month-old Gabrysia Filarowski, from Horsforth, Leeds, has Double Inlet Right Ventricle, a very rare heart defect.

She has been waiting for a transplant since October and in May she was put at the top of Britain's transplant list.

Gabrysia was taken to Newcastle's Freeman Hospital after a heart was found and surgeons started operating on her in the early hours of Friday.

Her mother Angela confirmed that the operation was taking place.

Speaking in May Mrs Filarowski said: "Since Gabrysia was born it's been the most amazing time but always completely consumed by the stress of her condition, constantly watching to make sure we're alright, it just has been never ending."

The family have been travelling about 100 miles from Leeds to Newcastle for Gabrysia's weekly blood tests

In October a consultant gave her parents the devastating news that she might not live another year.

She underwent open heart surgery when she was six days old, had another major operation three months later and doctors said an urgent heart transplant would be the only way to save her life.

Angela and husband Andrew have been anxiously awaiting a phone call from the Newcastle Hospital ever since.

Mrs Filarowski said: "If the telephone rings, your heart misses a beat. We have no idea if it's going to be mum or whoever.

"If we get the call, the operation needs to happen within three or four hours so we have our bags packed and at the ready."

Despite being born with the condition Gabrysia – also known as Gabriela - enjoys life and can sit up and play with her toys.

Mrs Filarowski, 31, said: "She is a very happy baby and just brings so much joy to our lives.

"Even though she is so poorly, she has lots of energy. She is on 25 medicines a day."

The couple have urged bereaved parents to consider donating their baby's organs for transplants, which they accept is not a subject easily discussed.

"For babies like Gabrysia it's her only chance. Nurses and doctors are afraid to ask parents to think about offering organs. We need to raise awareness about donorship."

Mrs Filarowski, 31, is a deputy headteacher at St Joseph's primary school in Hunslet, Leeds.

She and her husband, a technical director of the Society of Dyers and Colourists in Bradford, have added their names and that of their other children, Thomas, 11, and Ania, nine, to the online register of organ donors.

Mr Filarowski, 41, said he could understand why bereaved parents did not consider giving up their baby's organs.

He said: "Until we were in this situation we probably would have never considered giving up any part of Gabriela to be used as a transplant and yet there is no other hope for her.

"We have been told she has probably six months to live and so we need that heart and if there's a chance of continuing somebody's life surely that's got to give some sort of feeling of a young child's short life being of use for the future."