Answer: Ash
Ed plays "Meltdown" and "Orpheus" in his car, and a cover of "Everybody's Happy Nowadays" by the Buzzcocks plays when Shaun buys his mum some flowers. Chris Martin of Coldplay lends his voice to the cover and appears as himself promoting the charity "Zombaid" and as a zombie when Shaun and Liz ascend from the Winchester basement.
Ash started as a three piece outfit, Tim Wheeler, Mark Hamilton and Rick McMurray. The lads recorded two albums before recruiting Charlotte Hatherley, who worked with them for three albums, including the songs featured in "Shaun of the Dead". Hatherley then departed from the band, and the boys have since put out a further three albums.
Hatherley's mother, Patricia Franklin, can be seen in all three of the films in the "Three Flavours Cornetto" trilogy.
The band's first top 40 single, "Girl From Mars", is one of my favourite songs, and has been used by NASA as the hold music on their telephone lines.