After completing his apprenticeship, Grove was admitted as a graduate of the Institution of Civil Engineers, in 1839. A year later he went to Glasgow, gaining further experience in the factory of Robert Napier. In 1841 Grove had an affair with a woman called Elizabeth Blackwell, who gave birth to his illegitimate son, George Grove Blackwell, in March 1842. Between 1841 and 1846, Grove spent most of his time in the West Indies, as resident engineer during the building of cast-iron lighthouses. After this he joined the staff of the Chester and Holyhead Railway and then became assistant to Edwin Clark, working on the Britannia Bridge across the Menai Strait. An account of the first floating of the tubes of the bridge is recorded in "The Spectator" of 23 June 1849, which was Grove's first appearance in print. During this period, he lived in Chester, hearing music in the cathedral and also becoming familiar with Welsh folksong.