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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Chancellor George Osborne will seek to reassure financial markets on Monday morning following Britain's decision to leave the EU.
In his first outing since the referendum result, the lead Leave campaigner has outlined his vision for a post-Brexit Britain.