The son of a Norfolk farmer, he journeyed to India as ship's carpenter from which he earned sufficient funds to start his own building firm in Gray's Inn Road, where he was the first builder to have a 'modern' system of employing all the types of sub-contractors internally, on permanent wages, instead of outsourcing the tradeswork as had been done previously.
Cubitt's first major building was the London Institution in Finsbury Circus, built in 1815. After this he worked primarily on speculative housing at Camden Town, Islington, and especially at Highbury Park, Newington (now part of Islington).
His development of areas of St. Pancras, including Gordon Square and Tavistock Square, began in 1820, for a group of landowners including the Duke of Bedford.
He was commissioned in 1824 by Richard Grosvenor, the 2nd Marquess of Westminster, to create a great swathe of building in Belgravia centred around Belgrave Square and Pimlico, in what was to become his greatest achievement in London. Notable amongst this development are the north and west sides of Eaton Square, which exemplify Cubitt's style of buiding and design.
Cubitt was also responsible for much of Bloomsbury, and the east facing of Buckingham Palace. He also built and personally funded nearly a kilometre of the Thames Embankment.
He also was employed in the large development of Kemp Town in Brighton, and Osborne House on the Isle of Wight, completed in 1851.
Cubitt's public works included work on the provision of public parks, including being an organiser of the Battersea Park Scheme and a guarantor of the Great Exhibition of 1851, and contributing to the Metropolitan Buildings Act of 1855
After his death, Queen Victoria said "In his sphere of life, with the immense business he had in hand, he is a real national loss. A better, kindhearted or more simple, unassuming man never breathed."