Brennan was educated at St. Bede's Grammar School, Bradford, and graduated with a Bachelor of Law degree from Manchester University, where subsequently he was awarded an honorary Doctorate in 2000.

He was created Baron Brennan, of Bibury in the County of Gloucestershire on 2 May 2000[1] and is former President of the Catholic Union of Great Britain.

In 2006 Lord Brennan was appointed Delegate for Great Britain and Ireland of the Sacred Military Constantinian Order of Saint George in succession to Anthony Bailey.

On 19 November 2007 Brennan collapsed in the House of Lords shortly after concluding a speech on the Human Fertilisation and Embryology Bill.

Having been fitted with a pacemaker at St Thomas' Hospital, he was thanking peers and staff who had been involved in the occasion when he was last taken ill when he fell back in his seat.