After attending Upper Canada College and Osgoode Hall, he established a law practice in Cobourg, Ontario.

Despite elected as an opponent of the Macdonald–Cartier administration, Cockburn switched allegiances and became a supporter of Macdonald's Liberal-Conservative Party.

He was nominated by Sir John A. Macdonald to be Canada's first speaker of the House of Commons, a position in which he served from 1867 to 1874.

Cockburn lost his seat in the 1874 election that had been precipitated by the Pacific Scandal and that brought down the Macdonald government.

He resigned in 1881 when he was appointed to collect and classify Canadian statutes but this assignment was cut short by his death.