Possible Clues:

• 'Senses Working Overtime' band
• 'The Mayor of Simpleton' band
• UK rock band with the double entendre song "Pink Thing"
• "The Mayor of Simpleton" band
• Onetime British band whose name consists of letters suggesting 'bliss'
• 'Skylarking' band
• They also recorded as the Dukes of Stratosphear
• Beatles classic from A Hard Day's Night
• They also recorded as The Dukes of Stratosphear
• New Wave band with the hit 'Dear God'