He was the third of eleven children born to Ellen (née Wallsh) and John McMahon Glynn; his father ran a large general store.

Glynn enrolled at Trinity College Dublin, graduating Bachelor of Arts in 1878 and also attending the King's Inns in preparation for a career as a barrister.

His aunt Grace Wallsh had migrated to South Australia in the 1860s and was a member of the Sisters of St Joseph of the Sacred Heart.

In 1887 Glynn's easy personal manners and prominence as an editor assisted him in his election to the South Australian House of Assembly as the member for Light.

[1][2] In the chamber Glynn was an unwavering advocate of free trade, but his support of female suffrage and land nationalisation isolated him from his conservative colleagues.

He made major contributions to Murray River water rights, and advocated standardisation of rail gauges and universal suffrage.

[4] He protested the Constitution licensing the first Governor General to appoint a prime minister and cabinet prior to the first election as "opposed to all our notions of parliamentary government".

[5] In the struggle over question of Federation in Western Australia, Glynn with some deviousness secretly drafted a petition, signed by 28,000, which implored the British government to carve out of the goldfields a new colony, 'Auralia'.

Such a new colony would not serve Federation but its possibility was judged by Federationist strategists as likely to induce some Western Australians to support joining the new Commonwealth.

In 2016, the Australian Catholic University established a new public policy think tank based at its North Sydney campus, which was named the PM Glynn Institute.