Cornish joined the Navy in 1728, and having been promoted to lieutenant in 1739, he served at Cartagena in 1741. In 1742 he became flag captain of HMS Namur under Vice-Admiral Thomas Mathews and served with him in the Mediterranean. He was given command of HMS Guernsey later that year and commissioned HMS Stirling Castle in 1755. In 1758 he transferred to HMS Union.