When Meredith Edwards was deputy secretary in the Department of the Prime Minister and Cabinet in the 1990s, her boss, Max Moore-Wilton, told her that despite her outstanding performance, she would rise no further under the Howard Government, because of her "antecedents", her "genes".

Being a Burton made her and the rest of the family perennial persons of interest.

Soon after John Burton's death, Desmond Ball stated in an article for the Australian in 2011 that he had "probably" been a Russian agent, citing a statement Burton made at the 1954 Petrov Inquiry. Pam Burton, a Canberra barrister, consulted the transcript of evidence and revealed Professor Ball's errors in her own article in The Australian.

When Pam confronted Ball at a party in 2013 and demanded a retraction and apology, Ball refused. He later claimed he had never said Burton was a spy or a Communist, added that he shared John's views and values, and was just "having a stir". Pam wrote up their exchange in 2014 for Honest History. She later discovered that Ball had been an informer for ASIO in his honours year at the Australian National University.

Determined to correct the public record, she and Meredith have written the present book, with its inspired, ambiguous title. The people in it were "left-wing ratbags" to Quadrant writers, and persons of interest to ASIO.

The Burtons' and their friends' ideas were ahead of their time, and hence "subversive". They remain interesting persons today, when Australians are again warned that Communist China is our enemy.

Cecily Nixon and John Burton met in John Armstrong's philosophy class at Sydney University in 1934. Both their families were Methodists. Burton's father was a missionary in Fiji, where he emphasised social welfare over religious conversion. He inherited his preaching style, but came to see religion as a source of conflict. Instead, he advocated economic advancement and raising living standards as the way to achieve world peace.

Cecily, the daughter of a country doctor and a Sydney nurse, married John in 1939 in London where he was doing post-graduate work at LSE. Back in Australia, John joined the Department of External Affairs as its first and only economist, rising rapidly as a protégé of the Minister, Herbert Evatt, with whom he went to San Francisco for the drafting of the UN Charter.

In 1947, at 32, he became Secretary of the Department, and installed his wife and daughters on an innovative experimental farm in the Melrose Valley.

"Planet John" was inspiring, but self-centred; others circling around him became his disciples, or lovers. While Cecily coped with illness, John's absences and sudden moves to other houses for 30 years, she supported his projects - including standing for repeated elections, and running the Green Square Bookshop in Kingston, which supplied books and records by bus to school libraries and workers in the Snowy Mountains.

She typed and edited all his manuscripts, while always feeling misunderstood and undervalued. But she had her own aspirations to consider, and despite their thriving social life, the Burtons were not communicating well.

These, of course, were the decades of free love and newly reliable contraception, which Pam and Meredith don't mention. But they candidly describe affairs - mostly his - that led eventually to separation, divorce and remarriage on both sides. The middle daughter Clare, they say the cleverest of the three, influentially advanced gender equity, before her sudden death from cancer in 1998. She argued with John, who sought human progress and conflict resolution world-wide, but didn't understand feminism. Cecily found her forte in, of all things, relationship counselling.

Burton's innovations in foreign policy set us an example now. He advocated recognition of China in 1949, pressed Evatt to support independence for Indonesia, Vietnam, and Malaya, and advised Menzies against joining the Korean war. In the mid-1950s he called for Australia to be part of Asia, and attended Nehru's Afro-Asian conference in 1954 and Sukarno's Bandung Conference in 1955 - whose principles for peaceful co-existence remain in place today, including in China. He prophetically warned that the ANZUS Treaty could involve Australia in American antagonism towards Asia. "Deterrence", Burton wrote later, "doesn't deter".