Tennis legend Margaret Court's leaked appointment to the Companion (AC) of the Order of Australia triggered outrage because of her steadfast opposition to same-sex marriage and LGBTQ rights.

Revered journalist Kerry O'Brien will refuse his Australia Day honour in protest.

Canberra doctor Clara Tuck Meng Soo, who underwent gender transition in 2018, is handing back the Order of Australia medal she received in 2016 for her work as a medical practitioner with minority groups.

Federal MPs from across the political divide have thrown their weight behind an overhaul of the honours system.

Prime Minister Scott Morrison said last week the program recognised Australians from across the full spectrum of achievement.

Federal Opposition Leader Anthony Albanese and Victorian Labor Premier Daniel Andrews have lashed Court's AC, which comes after she was previously appointed an Officer (AO) of the Order of Australia.

Women received just over one third of the awards, prompting Governor-General David Hurley to concede more action was needed to boost gender equality.

"I am determined to make sure that the Order of Australia reflects the diversity and breadth of our community," he said.

"More needs to be done to achieve gender parity and increase diversity in other areas."

The decision to honour men's rights activist Bettina Arndt on Australia Day last year ignited a political firestorm later fuelled by her insensitive comments about a domestic violence murder.

Former prime minister Malcolm Turnbull, who was on the other side of the net to Court during the same-sex marriage debate, joins her as one of four people to receive an AC in 2021.

Mr Turnbull's government ultimately legalised same-sex marriage but his critics point to the postal vote in the lead up as a deep source of hurt for many in the LGBTQ community.

Since leaving politics in 2018, he's been an advocate for action on climate change and a strident critic of Rupert Murdoch-owned media's influence on politics.

While the focus has been on Court's views off the court, her record of 24 grand slam singles titles remains unequalled by any man or woman.

Elsewhere on the Honours List, trailblazing mathematician Cheryl Praeger has been appointed to the Companion (AC) of the Order of Australia.

The internationally-acclaimed researcher's work developed new algorithms used in computer systems by mathematicians and scientists worldwide.

A school career adviser almost nipped in the bud her remarkable journey after telling her girls didn't do maths as a profession.

But Professor Praeger defied the sexist advice to become one of the first females to hold that academic rank in mathematics during the early 1980s.

Rabbi John Levi has also received the highest honour for his service to the Jewish community.

The Australia Day awards recognise 844 people across a wide range of fields spanning politics, sport, arts, medicine, education, business and community service.

The list includes the first recipients being recognised for their efforts during the Black Summer bushfires and the coronavirus pandemic.

More than 43 per cent of awards were for outstanding service or achievement in the community.

Melbourne Cup-winning horse trainer Gai Waterhouse has been appointed an Officer (AO) of the Order of Australia with 130 Group One race wins under her belt.

Also a role model for women in sport, former Diamonds netball coach Lisa Alexander has been appointed Member (AM) of the Order of Australia.

The same honour was bestowed on former Socceroo Craig Foster who has also been recognised for his service to human rights and refugee support.

Ex-Australian Test cricket captain Greg Chappell, Socceroos great Tim Cahill and champion lawn bowler Karen Murphy were among the other sporting recipients of the honours.

Former South Australian premier Jay Weatherill is among the honours along with Lorrae Desmond, who played Shirley Gilroy on A Country Practice and was the first woman to win a Gold Logie.

Australian Associated Press