
If I sell my car, by law do I have to declare this and pay income tax to the Inland Revenue?
No, you only need to do this if you are disposing of an asset, and even then you would only pay tax on the profit generated. It is unlikely that you would make any profit on selling a car! Cars tend to lose value the older they get.
Essentially, an assett is something you own purely for the purposes of gaining capital - so things like a second home (which you rent out) or a car that you own purely to operate a taxi business would be considered an assett.
Your own car is just a personal posession, so if you sell it there is no tax implication.