After training as an artist Brierley went to Plymouth to study naval architecture and rigging, and in 1839 exhibited his first pictures at the Royal Academy. He travelled extensively. In 1841 he sailed to Australia and again in 1848 when the Royal Naval Surveyor, Captain Owen Stanley, offered to take him in HMS 'Rattlesnake' on a survey of the north and east coasts.

Many of his drawings were made into lithographs, in particular those depicting the navy during the Crimean War, and some were published in the Illustrated London News. In 1874 he became Marine Painter to Queen Victoria and was knighted in 1885. From 1884 until his death in 1894, he was Curator of the Painted Hall and its paintings at Greenwich Hospital.