Mr Brown, who is expected to succeed Tony Blair as prime minister, learnt of the condition of his four-month old son Fraser soon after his birth following a series of blood tests.

It is the second devastating tragedy to hit the Browns. In 2002 they lost their first baby, Jennifer Jane, who was born seven weeks premature and suffered a brain haemorrhage shortly before she died. They have a two-year-old son John who is fit and healthy.

A Treasury spokesman said tonight that Fraser had been diagnosed with cystic fibrosis. But he was healthy and “making all the progress you would expect a little boy to make.”

He added: “They were told in late July that Fraser may have cystic fibrosis. Tests sinced then have confirmed this. Thousands of other parents are in the same condition. They are confident that the advice and treatments available, including proper exercise and later sporting activity will keep him fit and healthy.

“The NHS is doing a great job and Gordon and Sarah are very optimistic that the advances being made in medicine will help him and many others, and they hope to be able to play their part in doing what they can to help others.”

Cystic fibrosis is the UK’s most common life-threatening inherited disease and affects more than 7, 500 babies, children and youg adults. Average life expectancy is now 31.

The symptoms can include poor weight gain, troublesome coughs and repeated chest infections.

Fraser Brown was born in July at Edinburgh’s Royal Infirmary. He weighed a healthy 7 lb 14 ounces. The condition was picked up in the routine series of blood tests that all babies in Scotland undergo.

The news shocked Westminster tonight, particularly as it dawned that Mr Brown would have known of the tragedy in the middle of Labour’s leadership crisis in the early autumn when he was accused by some MPs of plotting against Mr Blair. Members of the family have been told that Fraser is as yet showing no obvious symptoms of the diease. He has been putting on weight in the same way as other youngsters, but he has been to hopspital several times to help him overcome small infections.

The Brown’s first child died ten days after she was born, on January 7 2002.

Jennifer Jane weighed only 2lb 4oz when she was born by emergency Caesarean section on December 28 2001. This followed an ultrasound scan showed that she was not growing in the womb and had developed an irregular heartbeat.

After her birth doctors said that her prognosis was good. She recovered from a bout of jaundice, managed to breathe independently and put on some weight.

With her daughter apparently gaining strength, Mrs Brown, then 37, was discharged from Forth Park Maternity Hospital in Kirkcaldy, Fife.

But the baby’s condition deteriorated the following day and she was taken by ambulance from Forth Park to the neo-natal unit in Edinburgh. Doctors said she had suffered a brain haemorrhage

The Browns spent three nights in a private rooms set aside for the parents of critically ill children. She died in her parents’ arms at 5.20pm.

The Chancellor and his wife had been at their daughter’s side throughout her treatment at Edinburgh’s Royal Infirmary. The baby was baptised on Sunday in a brief Church of Scotland ceremony with her parents and grandparents by her bedside.

In September this year Mr Brown recalled the death of Jennifer Jane. Mr Brown spoke sadly of the terrible moment when his 10-day-old daughter, Jennifer Jane, died.

“You never come to terms with it...you always know there's something missing...two weeks ago she would have been going to school for the first time. You know you try to do things that make life better so it's had a purpose...that something good can come out of tragedy.”

Close to tears, he added: “We had seven or eight wonderful days. We didn't know she was going to die...until the last few days...so we had very, very happy days. She was unblemished by the illness she had...she just looked beautiful and she died in our arms. It’s very tough for any parent faced with a loss you never expected, that's so surprising that you have to come to terms with.”

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