The Royal Navy has since the 18th century published a list — the inventively named 'Navy List' — of all commissioned officers and ships. The frequency of publication varied — historically, it was generally published quarterly; later, it switched to annual publication. Modern editions of the list are widely available in digital form; many but not all older editions have also been digitised by various archives (like Google Books or Archive.org); the rest may only be findable in physical archives.

You're in luck, though: Google Books has the December 1879 list fully digitised, and pp. 191-263 include a list of every commissioned ship, including tonnage, armament, current duty station and personnel information.