Ms Dahl said: "The walls are cracking and you can smell the decay. We are trying to raise £500,000, which sounds a great deal of money, to try and move the interior of the little hut. It has to be done very, very carefully, in an archaeological way by archivists."
Today was flooded with critical emails and tweets.
The broadcaster Matthew Sweet asked: "Have I got this wrong? The international model and TV star Sophie Dahl is asking us for money to restore a shed?"
Another listener suggested Ms Dahl, married to the jazz singer Jamie Cullum, who is said to be worth £5m, could earn £250,000 from a single modelling job.
Others asked why the royalties from Dahl classics such as James and the Giant Peach, which sell more copies now than when he was alive, could not cover the cost.
The Roald Dahl Museum alone held £4.63m of funds last year, according to the charity's accounts. It generated £478,960 in revenue but managed to spend £550,900.
Sensing a carefully planned PR campaign turning into a disaster, the head of the museum took to the airwaves to clarify the position.
Amelia Foster said: "The Dahl family have given considerably to this project already and what we are not doing is going to the public and just saying, 'Help us raise this money.' We're actually going to trusts and foundations to support the capital costs for this.
"Obviously we'd welcome [public donations] but we're not going to the public saying, 'Gosh, you really need to help us.' We understand times are tight."
- INDEPENDENT