Having been born in Gateshead, Adamson moved to Lisbon in 1803 where he stayed with his brother until he returned to England in 1807. After which he began to collect and translate Portuguese literature which he later published. In England he gained work with a Newcastle solicitor. This led to the role of Under-Sheriff which he held between 1811 and 1835. In 1813 he helped found the Newcastle Antiquarian Society of which he became Co-Secretary; in addition he was a member of the Society of Antiquaries of London. In 1825 he became Secretary of the Newcastle Literary and Philosophical Society. He also helped establish the Newcastle Typographical Society. From 1824 he worked as Secretary for the Newcastle and Carlisle Railway. In 1841 he was given the knighthoods of Christ and of the Tower and Sword by the Queen of Portugal. He died in Newcastle in 1855.