Depeche Mode is an English band. The other singer you're thinking of is Morrissey.

I think Dark Wave is a movement you'd be interested in. Germany and Scandinavia became embroiled in that trend. Actually I really like the rock band Sisters of Mercy, from that era. The band is from Leeds, UK, but singer Andrew Eldritch is fluent in French and German and he spent many years living in Hamburg. He often gives interviews on TV and radio in German.