The ads claimed the milk would improve children's learning and concentration because it contains omega-3 fatty acid, normally found in oily fish.
The campaign cost manufacturer Dairy Crest £2m, £500,000 of which was Lord Winston's fee, which he is believed to have donated to Imperial College London, where is a professor of fertility studies.
In the ads, Lord Winston is shown holding a bottle with a sign around the neck reading "clever milk" and saying: "Recent scientific studies suggest omega-3 may play an important role in enhancing learning and concentration in some children." The ASA said that these claims were misleading.
Sales of the milk have been steady since the ads aired, with annual sales at £12m.
In scientific trials, referenced by the campaign, children with learning difficulties taking 558mg of omega-3 everyday, along with other supplements, did see an improvement in their reading, spelling and behaviour.
However, the ASA ruled there was no evidence that the same benefits would be achieved with smaller amounts of omega-3 as contained in the St Ivel milk, as a child would need to drink litres of the milk everyday to obtain the equivalent amount.
The regulatory body said: "The overall impression of the ads, including the experts' endorsement of the claim and reference to the scientific studies in support of omega-3, was that the presence of omega-3 in St Ivel Advance might enhance children's concentration and learning."
Lord Winston, who has presented several TV medical series including 'The Human Body', 'Making Babies' and 'Superhuman', stands by the claims in the advertisements.
Winston said: "Before my agreement with St Ivel Advance, I had spent several years studying the benefits of fatty acids.
"There is published data in scientific literature, which demonstrates the strong evidence for the benefit of children taking omega-3."
A spokesman for Dairy Crest said there was strong evidence to support the ad's claim but it would abide by the ASA's decision and have already amended press ad and other advertising.
The Food Standards Agency and the Joint Health Claims Initiative, insisted last November there was no firm evidence that adding omega-3 to milk improves a child's intelligence.
Professor Mike Lean, a member of the JHCI expert committee and head of the department of human nutrition at Glasgow University, said: "It is very disappointing that somebody like Lord Winston has allowed his authority to be used in an ad, which could mislead the public.
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