Chambers was the son of a fisherman, John Chambers (dates unrecorded), and his wife, Mary Appleby (dates unrecorded) from Whitby in Yorkshire. His family were extremely poor and Chambers left school at the age of 8 to begin working as mariner. Shortly after he was sent to work at sea. Due to his small size, he was often ridiculed by his shipmates and was given undemanding work on board the ship. This enabled him to develop his artistic skills and he gradually began to make drawings for the captain and crew. He returned to Whitby when he was 18 and continued to sketch marine seascapes. In order to make a living he worked as a painter and decorator until he moved to Wapping in London in 1825.
In Wapping, Chambers befriended the owner of the Watermans Arms, Christopher Crawford (dates unrecorded), and was commissioned by him and various sea captains to make marine paintings. Shortly after he was introduced to the surveyor and panoramist Thomas Hornor (1785–1844), whom Chambers collaborated with on a project at the Colosseum in Regents Park which opened in 1829. By this time he had also become a scenery painter at the Royal Pavilion Theatre and was praised for how he mastered new techniques of perspective. Chambers only occupied this position for a short time, in order to meet the many requirements of his patrons including British Admiral Lord Mark Kerr (1776 - 1840). Through Kerr, Chambers obtained an audience with King William IV (1765 - 1837) and Queen Adelaide (1792 - 1849) who purchased four marine paintings from him, three of which have remained in the Royal Collection. The commision of his well known views of the Royal Naval Hospital at Greenwich were probably due to the influence of hospital administrator and watercolour painter Edward Hawke Locker (1777–1849).
Until the 1830s Chambers had worked mostly in oils, however he also began to experiment with watercolours. He often made sketching tours around England, but mostly focused on views of the Thames and Medway. During his career Chambers exhibited at the Royal Academy of Arts in London, the British Institute, the Royal Society of British Artists and the Watercolour Society between 1827 and 1840. He was elected a member of the Royal Watercolour Society (originally known as the Society of Painters in Water Colours) in 1834, the same year he first exhibited there. Chambers first son, George William Crawford Chambers (1829 - 1878), was also a marine painter.