SS (RMS) Peveril (I) No. 76307 – the first vessel in the company's history to be so named – was a packet steamer which was operated by the Isle of Man Steam Packet Company until she sank off Douglas following a collision with SS Monarch in 1899.

Constructed in 1884 by the Barrow Shipbuilding Company, Barrow-in-Furness, Peveril was launched on Thursday 24 May 1884. The Barrow Shipbuilding Company also supplied Peveril's engines and boilers. The Peveril was, like Fenella, schooner rigged.

The wheelhouse was situated amidships and there was a flying bridge for the captain. Four repeating telegraphs by Chadburn were installed allowing direct communication with the engine room.

Length 207'; beam 26'; depth 13'; with an i.h.p. of 1,200. Peveril had a design speed of 13.5 knots, but is recorded as reaching 15 knots on her acceptance sailing.

Her passenger accommodation was well appointed, with the upholstering carried out by Messers Townsend & Ward, Barrow. Peveril's lower saloon and ladies' cabins were heated by steam.

Passenger capacity is recorded at 559, which was 55 more than her older sister, Fenella. Peveril had crew accommodation for 30.

Sister ship to Fenella, Peveril was intended for general cargo work in the main season and for passenger relief service in winter. In addition to this, Peveril also performed numerous summer cruises and excursions between Douglas and Ramsey.

Peveril made her acceptance sailing from Barrow to Douglas on Saturday 21 June 1884, under the command of Capt. Keig. She left the Hilpsford Buoy at Ramsden Dock at 09:49, arriving at Douglas at 12:51, covering the 44 nautical miles at a speed of 14 knots (26 km/h; 16 mph).