The original firm of Mitchell & Neilson was founded by William Neilson & James Mitchell in 1836-37 making marine and stationary engines. In 1837 the firm became known as Kerr, Mitchell & Neilson when Stewart Kerr joined the firm.

Kerr, Mitchell & Neilson was formed in 1837 when Stewart Kerr joined Mitchell & Neilson who manufactured marine and stationary engines. In 1838 Walter Montgomerie Neilson (the son of James B Neilson) joined the firm and was called on to make the business a success. By 1840 James Mitchell and William Neilson left the company, which was then effectively dissolved. James B Neilson (who had largely financed the Neilson & Mitchell venture) and Stewart Kerr formed a new company Kerr, Neilson & Co working from the Hyde Park Street works making locomotives, marine and stationary engines, but operating at a loss.

In 1840 James Mitchell left Kerr, Mitchell & Neilson and the company was renamed Kerr, Neilson & Co. Walter Neilson took the locomotive building business further, wanting to build Scottish locomotives for Scottish railway companies who until then had to go to England for their locomotives. By 1843 locomotive construction had begun. James Mitchell returned to Glasgow and ran the financial side of the business as a partner and the company became known as Neilson & Mitchell once more.

Kerr, Mitchell & Neilson became known as Neilson & Mitchell when it is believed that Stewart Kerr left the business. Marine and stationary engines continued to be made until 1855 when the company began to turn all its efforts to locomotive building. In 1855 the company became known simply as Neilson & Co.

In 1855 Neilson & Mitchell became known as Neilson & Co. Until 1858 James Reid had been the works manager at Neilson & Co. As the company turned exclusively to locomotive production, Henry Dubs who had more experience of designing & building locomotives replaced Reid. James Reid went to work for Sharp Stewart & Company in Manchester while Henry Dubs was made a partner in the Neilson & Co. business. Initially locomotive manufacturing by Neilson & Co was primarily for local Scottish railways. However, by the 1860's the company had established a large reputation in the export business, particularly in India and later in England and Europe. Later still, the company had a presence in Africa, South America and Japan. Neilson & Co also made small industrial locomotives. By 1861 the business needed to expand and so the company moved to new purpose built premises at Springburn, Glasgow named Hyde Park Works. This works eventually became the largest locomotive works in Britain. However, by this time the relationship between Walter Neilson and Henry Dubs was becoming increasingly strained. Dubs left the company in 1863 to set up his own company, Dubs & Co, taking key Neilson & Co staff with him. James Reid, who had gained a great deal of knowledge about locomotive building during his time at Sharp Stewart, returned as managing partner. By 1872 bitter resentment had come between Reid and Neilson regarding James Reid's option to buy Neilson out of the partnership. By 1876 Reid had become the sole proprietor, which continued until 1893 when James Reid's four sons became partners. Hugh Reid, the eldest son, became the senior partner on his father’s death in 1894. In 1898 the company changed its name from Neilson & Co. to Neilson, Reid & Co.

In 1898 the company changed its name from Neilson & Co to Neilson, Reid & Co. When the company became part of the North British Locomotive Company in 1903, Neilson, Reid & Co employed 3500 people and was producing around 200 locomotives a year. The works retained the name Hyde Park Works at amalgamation.