Adamson was born in Shildon, County Durham, on 30 April 1820. He was the 13th of 15 children – seven boys and eight girls – born to Daniel Adamson, landlord of the Grey Horse public house in Shildon, and his wife, Ann. Adamson was educated at Edward Walton Quaker School, Old Shildon, until the age of thirteen, when he left to become an apprentice to Timothy Hackworth, engineer to the Stockton and Darlington Railway, with whom he went on to serve as a draughtsman and engineer. By 1850, he had risen to become general manager of the Stockton and Darlington engine works (Soho Works, Shildon), and moved to become manager of Heaton Foundry in Stockport.
In 1851 he established a small iron works in Newton, Cheshire, expanding it a year later by building a new foundry called the Newton Moor Iron Works on Muslin Street (now Talbot Road), between Hyde and Dukinfield. He specialised in engine and boiler making, initially following designs created by Hackworth, making and exporting the renowned "Manchester Boilers". Adamson was able to experiment with the newfound wealth from the worldwide export of these boilers which incorporated ring joints in the form of his patented Anti-Collapsive Flange Seam. He was also one of the pioneers of explosive forming used in the foundry process.
In 1872 he designed and built the Daniel Adamson and Co factory, a new premises in Dukinfield next to Dewsnap Farm (off Dewsnap Lane), with its entrance on Johnsonbrook Road. This new works was approximately 1,000 yards (910 m) from the old foundry but the site was large and had enough spare land around it for any planned expansion.
He improved the design and manufacturing process (pioneering the use of steel and taking out 19 patents in the process) over the 36 years he was involved with boiler and other foundry manufacturing. When he died in 1890 the business employed some 600 people.