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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Accompanied by the Duke of Edinburgh, the Queen will attend the opening ceremony of the fifth session in the Holyrood chamber.
Ms Leadsom has received the backing of Ian Duncan Smith, the former work and pensions secretary.
The former shadow work and pensions secretary is considered a more viable candidate than Angela Eagle, a Labour source has told ITV News.