Lead man Mike Scott is, afaik, the only consistent member of the band, and must have burned through a couple of tens of musicians. The Whole of... must be their archetypical early Waterboys song.
Elastica with Waking Up.
UK alternative rock band, London based. Frontwoman is Justine Frischmann, ex-Suede. Waking Up is from the debut album Elastica, released in 93.