William Andrew Veitch was born on 25 May 1870 at Port of Monteith, Perthshire, Scotland, the son of Stephen Veitch, a schoolmaster, and his wife, Janet Davidson. After attending his father’s school, he worked for the post and telegraph office until 1887, when he emigrated to New Zealand. He tried his hand at gum-digging and then became a telegraph boy. In January 1889 he began a 22-year career with the government railway service, working his way from cleaner to engine-driver by 1908. Apart from two years in Canterbury, he was stationed in various North Island towns. At Aramoho, Wanganui, on 7 April 1896, he married Emma Elizabeth Gurr.
An active member of the Amalgamated Society of Railway Servants of New Zealand (ASRS), Bill Veitch served as secretary of the Cross Creek branch (1904–6) and as chairman of the Wanganui branch (1907–8) before becoming national president in 1908. He was also a member of the Government Railways Superannuation Fund Board and the North Island Railway Appeal Board. According to a union delegate, he showed 'moderation and reasonableness' in his dealings and 'was not given to extravagance of method or language'. During his four years as president he oversaw a major restructuring of the ASRS and in 1910–11 he presented petitions to Parliament seeking improved wages and conditions. Frustrated by the government’s failure to deal with the railwaymen's grievances, and believing that political rather than industrial action was the way to improve the position of working people, he contested the Wanganui seat at the 1911 general election. Standing as an independent labour candidate, he topped the poll on the first ballot and defeated the sitting Liberal MP, J. T. Hogan, at the second.
In return for Reform Party support at the second ballot, Veitch had pledged to vote against the Ward government in a no-confidence motion. This he did on 27 February 1912, but two days later he voted with the government. Not bound to any party, for a time he seriously considered joining a reconstructed Liberal government. Instead, in April 1912, he became an executive member of the newly formed United Labour Party of New Zealand.
Veitch attacked the power of the 'party boss system' in decision-making and suggested that the prime minister and cabinet be elected by MPs. He also advocated a system of proportional representation in which each section of the community would send its own member to Parliament. A strong opponent of commercial monopolies, he proposed that the Court of Arbitration be given extended powers to 'fix the relations between wages and prices’. In 1912 he sat on the Royal Commission on Cost of Living in New Zealand, which supported his claim that some monopolies had forced up prices.
Veitch attended the labour movement’s Unity Congress in July 1913, but walked out with other moderates opposed to the centralised control of strikes, and rejected the new Social Democratic Party. During the waterfront and general strikes later that year, he again argued that the arbitration system should be reorganised to deal with 'the causes of such difficulties’. He held his seat at the 1914 election as an independent labour candidate, but broke with the political labour movement in 1916 over its opposition to conscription. Standing in 1919 as 'Moderate Labour’, he was returned with the support of the local Liberal organisation. In Parliament he became part of a loosely organised group of moderate labour and Liberal members; in 1922 he was re-elected as a 'Liberal Labour’ candidate.
In 1925 Veitch finally joined the Liberals, at that time known as the National Party. He became its nominal organiser and held Wanganui at that year’s election, but only 11 of the party’s candidates were returned. Dissatisfied with the party’s performance, and convinced that the Reform government was interfering with individual liberties, by March 1927 he had begun a campaign to revive the Liberal Party. Touring the country, he held meetings six nights a week to organise 'groups of Liberals who could set about selecting candidates’. In April 1928 he linked up with the United New Zealand Political Organisation, which had been set up in August 1927 by A. E. Davy, Reform’s organiser in 1925. In the months leading up to the 1928 election, Veitch, Davy and National leader George Forbes drew the disparate forces opposed to Reform’s 'socialism’ into the new United Party.
Veitch was one of four candidates for the party’s leadership in September 1928, when Sir Joseph Ward was elected. After United became the government in December, he served as minister of mines, labour and transport in the Ward ministry (1928–30), then as minister of railways and transport under Forbes (1930–31). In 1931 he lost these portfolios to make way for Reform MPs after the formation of the coalition government. Although re-elected that year, much of his traditional working-class support went to his New Zealand Labour Party opponent.
Veitch voted with the coalition government until it devalued the currency in January 1933. Unhappy with the measure, he and four other MPs unsuccessfully tried to persuade William Downie Stewart to lead a new party. Veitch regarded devaluation as 'a narrow, class-conscious policy’ that bled urban dwellers for the doubtful benefit of farmers and set 'one section of the people against another’. After voting against the Banks Indemnity (Exchange) Bill in February, he was excluded from the coalition caucus.
By 1935 Veitch had joined the anti-socialist Democrat Party, and in November he lost to Labour the seat he had held for 24 years. Until then, Wanganui electors had voted for Veitch personally rather than for the grouping or party he belonged to. He later claimed this was because he spoke his mind openly and honestly on all questions. Despite standing under numerous political labels, he had been a consistent and implacable opponent of any group, doctrine or legislation he saw as a threat to individual rights. In this he regarded himself – and was seen in Wanganui – as the legitimate Lib–Lab successor to John Ballance. Veitch would have been more comfortable in the parliaments of the nineteenth century, but in 1935 there was little room for maverick MPs. He tried to re-enter Parliament in 1943 as the New Zealand National Party candidate for Wellington Suburbs, but failed.
Outside national politics Veitch served on the Wanganui Harbour Board and the Wanganui River Trust Domain Board. In 1917 he stood unsuccessfully for the mayoralty. He was interested in rowing, and was one of the founders of the Aramoho Boat Club. After the death of Emma Veitch in 1944, he married Ann Sinclair Davidson in Dunedin on 19 May 1951; she died in 1959. William Veitch died, aged 90, at Paraparaumu on 1 January 1961, survived by three sons and three daughters of his first marriage.