David Mellor recalled the former sports minister's reaction to reports that Mr Mellor had been caught in bed wearing a Chelsea strip with an out-of-work actress.
"Tony told me he did not believe that. It could not have been a Chelsea shirt because no one in a Chelsea strip could score five times."
John Prescott, Tessa Jowell, Margaret Beckett and Alastair Campbell were among Labour figures at the funeral at the City of London Crematorium.
But in a testament to the universal appeal of the man, it fell to the former Tory minister to deliver the most memorable eulogy. "A lord of misrule, a cheeky chappy, call him what you will - he can be defined but he cannot be replaced," said Mr Mellor.
Having retired from the Commons after more than 20 years at the last general election, Mr Banks accepted a peerage as Lord Stratford. He died earlier this month in Florida, aged 62, after suffering a stroke.
Mr Mellor spoke about his friend's "glorious simplicity", saying he had no side, no pomposity and certainly no self-love.
Mrs Beckett said: "If ever a phrase was coined to describe one person, it's the words 'lovable rogue'. That is how I will remember him. He believed in debate and the battle of ideas. He respected his opponents and they reciprocated."
She pointed out that those who were criticised by him, such as the Tory MP Nicholas Soames - dubbed the one-man food mountain - wore their Tony Banks insults like a badge of honour.
Others present at the funeral included Richard Caborn, the sports minister; David Davies of the Football Association; Tony Benn, the former Labour MP; and Chris Smith, the former culture secretary.
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