Smirke was the son of portrait painter Robert Smirke, and studied architecture as a pupil of classical architect John Soane in 1796, the same year he commenced his studies at the Royal Academy. He also studied and travelled in southern Europe for several years.
Smirke designed public buildings in the classical style, including the main block and facade of the British Museum, the east wing of Somerset House and the adjacent King's (formerly Smirke) Building of King's College London, and the Royal College of Physicians building in Trafalgar Square (now known as Canada House).
His domestic buildings were often in the Gothic style. Lowther Castle in Cumbria was his first job, in 1806, when he was just 25. Eastnor Castle was designed by him in the early 19th century.
His buildings outside London included the Shire Halls of Gloucester, Shrewsbury and Hereford, plus alterations to Luton Hoo house.
He also designed the second incarnation of the Covent Garden Theatre, now the Royal Opera House (destroyed by fire in 1857), and the General Post Office building in St Martins-le-Grand in the City of London (built between 1825 and 1829 (demolished c. 1910).
Together with John Nash and Sir John Soane, he became official architect to the Office of Works in 1813. He advised the Parliamentary Commissioners on the building of new Churches from 1818 onwards, contributing four himself, including St George, Brandon Hill in Bristol.
He was knighted in 1832, and received the RIBA Royal Gold Medal for Architecture in 1853.
His brother Sydney Smirke was also an architect, best known for the circular reading room at the British Museum.
He died in Cheltenham on April 18th 1867.
