He started his career as a watchmaker and a few years later was articled to Alexander Kennedy Smith, a renowned civil and mechanical engineer of the period.

Brennan spent some years working out his invention, and received a grant of £700 from the Victorian government towards his expenses.

Sir Andrew Clarke alerted the authorities to the possibilities of the torpedo if used in the defence of harbours and channels, and the patent was eventually bought for a sum believed to be more than £100,000 (£ 12,843,000 in 2025).

At the Japan–British Exhibition of 1910 at White City, London, he built a mile long monorail track and gave rides for around 40 people at a time on his gyro stabilised 22-ton prototype.

[4] Brennan was buried at St. Mary's Roman Catholic Cemetery, Kensal Green, London, in an unmarked plot numbered 2454 that is opposite the Chapel record office.

[7] On 11 March 2014, Irish Taoiseach Enda Kenny unveiled a new gravestone for Brennan at St. Mary's in a ceremony honouring the inventor's life and career.