When steel entered Victorian ship construction

Was mild steel used in ship construction during the mid-to-late nineteenth century?

Yes. From about 1855 onward, Bessemer steel increasingly replaced iron in later nineteenth-century shipbuilding.

Particular fittings, cables, pins, and hinges make a general answer difficult. After an initial correction to the century under discussion, the Bessemer process emerges as the decisive change: from roughly 1855 onward, steel increasingly displaced iron in ship construction. A precise date range matters because the later Victorian navy underwent a rapid material transition.