He was educated at St Alban's RC High School in Pontypool and Pembroke College, Oxford, graduating with a degree in Philosophy, Politics and Economics in 1982.

[3][4] In July 2002, Brennan appeared in the House of Commons without a tie and called for Westminster to have "dress down" Thursdays, stating that Billy Bragg had complained Parliamentarians gave a "besuited image that's male, pale and stale".

[17][18][19] Brennan was made Shadow Minister for Trade, Investment, and Intellectual Property by Jeremy Corbyn in September 2015.

[20] He resigned from this position on 28 June 2016, following a motion of no confidence in Corbyn which was passed overwhelmingly by Labour MPs, 172–40, in a vote which was not binding.

[21] Brennan supported Owen Smith in the failed attempt to replace Jeremy Corbyn in the 2016 Labour leadership election.

[22] At the snap 2017 general election, Brennan was again re-elected as MP for Cardiff West with an increased majority of 12,551 votes.

[29] After Brennan carried out his threat to table the amendment, The Independent newspaper reported that Tony Blair faced the "biggest backbench rebellion" of his career.

The BBC said he was "instrumental in extracting the government's commitment to establish a £400 million fund to provide compensation for workers who lost their pensions when their firms went bankrupt".

Brennan said he bought from businesses in his constituency but the items were for use in his second home, calling the story a "smear with no basis in fact".

[31][32] In 2014, Brennan led a campaign with musician Billy Bragg to lift a blanket ban on prisoners having access to guitars.

[33] Brennan held a Westminster Hall debate on the subject to try and get the government to overturn the ban, citing the importance and the efficacy of music as a means for the rehabilitation for prisoners.

[35] In late 2024, Brennan was nominated for a Labour Party life peerage by Prime Minister Keir Starmer.

He is also a member of a parliamentary rock band MP4 with fellow politicians Ian Cawsey, Pete Wishart and Greg Knight.