They attended the Rugby World Cup at Twickenham, happily posing for pictures.

The relationship is 84-year-old Murdoch’s first foray into the dating world since he split with Chinese-born American businesswoman Wendi Deng in 2013.

Ms Hall, 59, is the former wife of Rolling Stones frontman Mick Jagger.

The relationship with Ms Hall is proof Murdoch is “as vigorous in his private life as he is in business”, a source said, according to the AFR.

Mr Murdoch has been married three times, the first to Patricia Booker in 1956.

They divorced in 1967 and Mr Murdoch married Anna Torv, a Scottish-born cadet journalist working for The Daily Telegraph, later the same year.

They divorced 32 years later and Mr Murdoch married Ms Deng later the same year in a relationship that would last 14 years.

It ended around the time an article was published inThe Mail on Sunday reporting Ms Deng was “infatuated” with former Prime Minister Tony Blair.

Ms Hall was married to the Rolling Stones frontman for nine years before they split in 1999.

“It’s all very new. They are really enjoying each other’s company very much,” a close friend said of the pair.

“He is very fond of her. There is no question that they are a couple.”