Do you live in a gated estate, or does it have open access to the public? If it's open to everyone, then it's defined as a public space, and your car needs to be taxed and insured, even if it's left in a parking space.
Well yes and no. It's a private car park, there a signs everyone saying so. But the public can drive in and pay as the car park is protected by a barrier and operates on a ticketing system.
Your last sentence about a car requiring tax is not true if it's in a private space, but that space is in a public car park. You can't be clamped or ticketed for parking in/on your own property. This is something ive looked into in the past. What you are basically saying is anyone living in an apartment complex who owns a car can NEVER declare their car off the road.