Born to convict parents on July 15, 1846 at Launceston, Tasmania, he followed his father's trade as a bootmaker. Largely unschooled, barely literate, and with poor eyesight, Trenwith had a gift for oratory and public speaking which was to assist him in union organising and later as a politician. He was involved during the late 1870s with the National Reform League where he agitated for protective tariffs, a land tax, and reform of the Victorian Legislative Council.
As one of the founding members of the Victorian Operative Bootmakers Union in 1879 he served as its Secretary in 1883. He was instrumental in coordinating the 1884 bootmakers' strike from Melbourne Trades Hall, which saw Victoria's first fullscale picketing and was an important campaign in the fight against sweated labour. He advocated the abolition of outwork in the bootmaking industry to eliminate cheap labour and encourage unionisation.
Trenwith honed his public oratory skills at North Wharf on the banks of the Yarra River, in Melbourne on Sunday afternoons, along with Joseph Symes, Chummy Fleming, and Monty Miller and many other Australian labour movement activists and radicals of the time.
In 1886 he was elected President of the Trades Hall Council, and was also made a Life Governor of the Homeopathic Hospital that year. By 1890 he was seen as a Trades Hall bureaucrat being opposed by radicals such as Chummy Fleming about working conditions, who accused Trenwith and other moderate THC bureaucrats, of 'working with blood-sucking capitalists.'
After a number of attempts at nomination, Trenwith was elected in May 1889 for the seat of Richmond (1889–1903) to the Victorian Legislative Assembly on a labour platform and sought reforms in education, unemployment and tariff protection. He was the lone labour representative in the Victorian Parliament until the following election in April 1892 when 13 labour aligned candidates were elected.
During 1892 Trenwith was elected leader of the Victorian Labour Party, but continued to have problems at the grassroots with strong opposition from public meetings chaired by Chummy Fleming. During the 1892 maritime strike he argued strongly for compulsory arbitration over direct action, much to the disgust of labour radicals. In 1893 Trenwith opposed Chummy Fleming's proposal for the affiliation of the Knights of Labor to the Trades Hall Council on the grounds that as a secret organisation it could not be organised industrially.
In the Parliament of Victoria Trenwith served as Minister for Railways, commissioner for Public Works and vice-president of the Board of Land and Works between November 1900 and February 1901 in the Sir Alexander Peacock ministry, and briefly as Chief Secretary (1901–02). The Government he was part of came under attack in November 1902 from a Trades Hall motion from Chummy Fleming protesting against the reduction of old age pensions from 10/- to 8/-.
Trenwith was the only elected labour representative at the Federal Constitutional Convention (1897–98) that led to the Federation of the six Australian colonies in 1901. His support of Federation was over the objections of many in the labour movement, and served to ameliorate accusations that the Federation Bill had been "wholly shaped in a conservative direction" as accused by the Age.
From 1903 to 1910 Trenwith served as an Independent Senator for Victoria. His withdrawal of support for the Federal Labor government of Andrew Fisher resulted in his defeat at the following election and retirement from politics.