Possible Clues:

• Touring car
• No tea served up on local transport
• Light four-wheeled carriage
• Sounds as if there's some fete on for such old transport
• Sounds as if you might have met your fate on this sort of transport
• One might drive it on after the fete, by the sound of it
• Carriage finds one path negotiable
• 4-wheeled carriage
• Carriage from Westminster heading north to a school
• Tortuous path, one taken in carriage