Possible Clues:

• What Thatcher is responsible for tortures those having to bear the baggage for the long road perhaps
• Vehicle accessories — OK for cars (anag)
• Storage attachments on cars
• For those hitting the road with The Gladstones, for example, it's on the house for those who can hold their drink
• On top of the jail perhaps holding one's drink can be useful for those planning an escape with getaway car perhaps
• Genesis clip with loud music torments those types with extra baggage on tour with The Cars
• Expressed regret over attempts to extract fuel for car parts
• Pop corks for a way of moving the cases from A to B?
• Last frames on the house for going on touring holiday?
• Cars may have these fitted for a trip through ice