Haysi Fantayzee

Here's a live performance by a New Wave band that has arguably aged less well than many others, such as Blondie and The Cars. The rest of their 13-track playlist is here.

Their Wikipedia page says:

Haysi Fantayzee was an avant-garde, new wave pop project emanating from the Blitz Kids street arts scene in London in the early 1980s. The group's music combined reggae, country and electro with political and sociological lyrics couched as nursery rhymes.[3]

Catapulted to stardom by their visual sensibilities, Haysi Fantayzee combined their extreme clothes sense – described[4] as combining white Rasta, tribal chieftain and Dickensian styles – with a quirky musical sound comparable to, but distinct from, other new wave musical pop acts of the era, such as Bow Wow Wow, Adam and the Ants and Bananarama