Gerry Anderson's son, Jamie Anderson, said he was "very sad" to announce the death of his father.
He confirmed he died peacefully in his sleep at midday today, after suffering mixed dementia in recent years.
A donation page dedicated to his memory and support of the Alzheimer's Society has been set up.
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The advertising watchdog has ruled the "beach body ready" campaign was not offensive or socially irresponsible.
Britain is set for the hottest day of the year today, with temperatures forecast to hit up to 34C (93F).
The Airports Commission is to publish its report and recommendations on whether an extra runway should be built at Gatwick or Heathrow.