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Former Australian Prime Minister Julia Gillard has warned Theresa May she may face growing "gender-based" criticism.

She told the Institute for Government she had also taken over "in a political crisis" and, at first, there had been little comment about being a woman.

But "the gender stuff grew over time, as the government I led dealt with the hard issues and got into politically choppy waters", she added.

Mrs May is the UK's second female prime minister, following Margaret Thatcher.

Ms Gillard, who, as Australia's first woman PM, was in power from 2010 to 2013, said female leaders had to labour under the stereotype that they should appear "empathetic and nurturing". If they gained high office, it appeared they "must have given up on the nurturing".

She said Democratic candidate Hillary Clinton was "suffering a bit from that" in her race against Republican Donald Trump for the US presidency.

Ms Gillard, who has warned that many women in public life face "almost daily" rape threats, told the audience in London that, while she was in charge of Australia, opponents held up placards bearing the slogan "Ditch the witch".

She offered Mrs May - who took over from David Cameron in July amid the political disruption following the referendum vote for Brexit - advice based on her experience.

She said: "What I actually found was, when I came to the prime ministership in a political crisis moment, my gender wasn't the focus of the reaction.

"Rather the gender stuff grew over time, as the government I led dealt with hard issues and got into politically choppy waters.

"The harder it got, it became more likely that gendered insult would become the political weapon."

Ms Gillard, who, like Mrs May, does not have children, said a typical comment on her during her premiership would have been: "She doesn't have children, so she doesn't understand ordinary people and their lives. She was ruthless in getting to the top, so everything she does is about her political interests."

She criticised Australia's male business leaders for not doing more to speak out against sexism during her time in office.

Ms Gillard, who is a visiting professor at King's College London, said more needed to be done to ensure women could balance family life with a career without suffering a lack of promotion.