There are multiple artists named Sinking Ships.

1) A hardcore band hailing from Seattle, Washington. In 2005 the band released their debut full length, Meridian, consisting of old demos and new songs.
At the end of 2005 Sinking Ships signed to seminal hardcore label Revelation Records. The band released their second album, Disconnecting, in July 2006.
After releasing two more 7 inches entitled "Ten" and "Safe" and also doing a split with Japan's My Love and As We Let Go, Sinking Ships called it quits in late 2008.

2) Sinking Ships were an English band formed in the fall of 1979, by ex Berlin members Simon Brighton (guitar) and Terry Welbourn (bass), together with Stress musicians, Colin Hopkirk (vocals) and Nick Green (drums).
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Artist biography from last.fm