Burton's best-known watercolours, The Aran Fisherman's Drowned Child (1841) and The Meeting on the Turret Stairs (1864; also known as Hellelil and Hildebrand) are in the National Gallery of Ireland.

A visit to Germany and Bavaria in 1842 was the first of a long series of trips to various parts of Europe, which gave him a profound knowledge of the works of the Old Masters.

[6][7] In June 1874, he obtained a special grant to acquire the art collection of Alexander Barker, which included Piero della Francesca's Nativity and Botticelli's Venus and Mars.

In 1876 a bequest of 94 paintings, mainly by Dutch artists but also including works by Pollaiuolo, Bouts and Canaletto, was made by the haberdasher Wynne Ellis.

[8] During the twenty years that he held this post he was responsible for many important purchases, among them Leonardo da Vinci's Virgin of the Rocks, Raphael's Ansidei Madonna, Anthony van Dyck's Equestrian portrait of Charles I, Hans Holbein the Younger's Ambassadors, and the Admiral Pulido Pareja, by Diego Velázquez (this subsequently attributed to Velázquez's assistant Juan Bautista Martínez del Mazo).