[9] In October 2013 Brady announced that he would seek to be the Fianna Fáil candidate in the Dublin constituency for the 2014 European elections but was unsuccessful.

[10] In October 2018, Brady announced his intention to seek the Fianna Fáil nomination for the Dublin constituency in the European Parliament.

[22] In March 2015 Brady launched Ireland's first community based rapid HIV testing programme, the Knownow project.

[25][26][27][28] The coalition government led by Prime Minister Malcolm Turnbull had a policy of holding a national plebiscite to decide the issue.

In the summer of 2017 the government announced it would hold a postal survey through the Australian Bureau of Statistics as a proxy public vote on the marriage equality.

[32][33] Brady had designed a campaign approach that focussed on fairness and equality as the key message delivered through human stories.

[43][circular reference] On the morning of the results Brady addressed a crowd of over 10,000 in Sydney with the clear message that Marriage Equality must be a moment of national unity and social peace and that people needed to reach out to those who had voted no in the survey and continue the work of persuasion.

[44] Australia joined Ireland as the only two countries in the world to pass marriage equality by a public vote and Brady has been at the forefront of winning both.

[48] The following Sunday, on his flight back from Dublin where the launch occurred, Pope Francis was asked what he would say to the father of a son who says he is homosexual.

"[49][50] Brady launched, with Italian Senator Monica Cirrinna and former President of Apulia Nichi Vendola, amongst others, the Equal Future Campaign's YouGov survey of attitudes in the Catholic world towards damage to children and young people from LGBT stigma.

[51][52] The poll found that half of adults across eight countries – Brazil, Mexico, the Philippines, the United States, France, Italy, Spain, and Colombia – agreed with the statement "It could be damaging to a child/ young person's mental health and well-being if they felt that being LGBT was a misfortune or disappointment,"[53] while 23% disagreed, and that 63% of practicing Catholics in those countries agreed that Catholic Church should reconsider its current teaching on LGBT issues to help support the mental health and well-being of children and young people.