The row continued off-air when a furious Mr Johnson swore at his Labour opponent.
Travelling up to the roof terrace to be photographed, the Mayor shouted at Mr Livingstone "it's all f****** lies, it's all f****** lies".
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New 'smart ticketing' plans will also be introduced so travellers can receive automatic compensation payments for late trains.
The 41-year-old father of six died last Thursday - a week before he and the band had been due to begin touring in North America.