Architectural historian and architect; first to record entasis in Greek temples. Cockerell was trained between1809-1810 by his father, Samuel Pepys Cockerell (1753-1827), to follow in his footsteps as an architect. He also studied with the architect of the British Museum, Sir Robert Smirke (1780-1867). Cockerell toured Europe between 1810-1817, sometimes delivering messages to the British fleet, but also visiting the regions of the Ottoman Empire and southern Italy. He met Lord Byron and his colleague, John Foster (1887-1846), the latter with whom he traveled. Cockerell's interest in Greece was to measure the architectural monuments, a purpose which allowed him to make several important discoveries for architectural and art history. After visiting the island of Delos, Cockerell and Foster moved to Athens, where they met the German archaeologist Jakob Linkh (1786–1841), Otto von Stackelberg (1787–1837), and Karl Haller von Hallerstein. The five traveled to Aegina in 1811 to excavate the temple there. Their discoveries included the pedimental sculpture from the temple, later identified as the Temple of Aphaia (Glyptothek, Munich). Next they traveled next to the Peloponnese where they discovered the Centauromachy frieze at the temple of Apollo, Bassai (British Museum, London). Cockerell continued on to Sicily where his facility for imagining buildings from their ruins was most aptly demonstrated. Returning to Athens, Cockerell discover the entasis in the columns of the Parthenon and the Erechtheion; although entasis had been known in Roman buildings, Cockerell was the first to notice this in Greek structures as well. In 1815 he moved to Italy, remaining there until his return to England in 1817. Cockerell worked as a practicing architect, producing designs for the Fitzwilliam Museum, Cambridge University, the Taylorian and Randolph buildings at Oxford, and restoration work of St. Paul Cathedral, London. His design for the Ashmolean Museum in Oxford, used the Ionic order and frieze he had observed at Bassai. Cockerell was part of a committee including Jacques-Ignace Hittorff and Thomas Leverton Donaldson, which met between 1836-1837 to determine whether the Elgin Marbles and other Greek statuary in the British Museum had originally been colored. They concluded that they had not, (their findings appear in the Transactions of the Royal Institute of British Architects for1842), despite Cockerell's knowledge that other sculpture had. In 1840 he was appointed Professor of Architecture at Oxford, a position he held until 1857 (Emeritus thereafter). He was made a member of the Society of Dilettanti the following year. Cockerell supplied the drawings supplement volume to James "Anthenian" Knight and Nicolas Revett's to The Antiquities of Athens, 1830. His survey of the sculpture and architecture of Wells Cathedral appeared in 1851. He is buried in St. Paul's Cathedral, near Christopher Wren's tomb.
As a practicing architect, he believed, with Vitruvius, that architects needed a deep and abiding respect for history. He was unswayed by the prevailing Gothic trend in architectural design. His diaries reveal a strong intellect and fastidious temperament. Cockerell knew J. W. M. Turner and planned for Turner to do the illustrations for his publications on Bassai and Aigina. Though Cockerell was the first to note entasis on Acropolis buildings, this discovery was first published in a work on the Athenian architecture by Francis Cranmer Penrose (1817-1903) in 1851, whose notes Cockerell had given to Penrose. Cockerell had discovered color residue on the Temple of Aphaia at Aigina, but again, it was other (Guillaume-Abel Blouet in 1832) who published the material.