Robin Gibb, 61, spent four days in hospital earlier this month suffering from inflammation of the colon.
The Bee Gees singer twin brother, Maurice, died of an intestinal illness in 2003.
But he later appeared on ITV’s Alan Titchmarsh Show, where he made no mention of his health problems.
However, he apologized on camera to the Prime Minister David Cameron for missing their meeting.
“Robin’s not well. He didn’t feel well enough to meet Mr Cameron and stayed at home for the morning,” said a source close to Robin Gibb.
“But by the afternoon, he felt well enough to go on the Titchmarsh show.”
Robin Gibb was taken to Radcliffe Hospital in Oxford on October 13, after suffering severe stomach pains at his home in Thame, Oxfordshire.
“This is what did it for his brother Maurice – but what is different is his condition was left for a long time and Robin’s has not been,” Robin Gibb’s manager said.
Robin Gibb was only discharged from hospital a week ago, but was determined to get back to work as he promoted his new charity single.
However, as the singer arrived at the ITV studios, it was clear his recent illness has taken its toll.
Robin Gibb’s wife Dwina had called the emergency services after he was “taken short with pains” at their mansion in Thame.
After this incident, Robin Gibb, who is estimated to be worth £110 million ($170 million), had to pull out of a BBC Songs of Praise concert.
The singer is said to be an ardent tee-totaller and vegan.
Robin Gibb’s manager explained: “Obviously it is a worry. This is what did it for his brother Maurice – but what is different is his condition was left for a long time and Robin’s has not been.
“Our concern is that it keeps recurring but he is determined to get better and we just hope things will be OK. Robin just wants to get back to work.”
In 2010, Robin Gibb had emergency abdominal surgery to remove part of his intestine after suffering excruciating pain at a concert in Belgium.
Afterwards it was revealed that if Robin Gibb’s condition had not been dealt with so promptly he could have been dead “in two hours”.
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