Paperwork
If you are bringing the car in yourself, you need to arrange temporary
transit plates (the dealer may charge an extra small fee for this) and
must have a Certificate of Conformity to prove that the car meets EC safety
and emissions standards.
Within seven days of the car arriving, you must declare it to HM Customs and Excise. On receiving all your receipts for petrol, travel tickets etc, that prove that you brought the car in yourself; they will send you forms to fill in. When these are returned, Customs will send you a bill for 17.5% of the car's price, which must be paid within 30 days.
Once you have a receipt for this payment (Customs and Excise form C&E 386), the car can be registered. Take all your documentation to a Vehicle Registration Office, and fill in the form V55/5 (a £25 fee), pay UK road tax and get number plates made up.
Buying from outside the EU - from Japan, for example - is more complex. If you can prove that you bought and owned the car abroad(i.e. you have your hotel and flight receipts and so on), you can bring in a car as a personal import.
If an agent brings in the car for you, to avoid paying another 10% tax (in addition to the standard 17.5%) it needs to be registered and 'owned' in another EU country - then it counts as their personal import according to EU procedure. This is why so many Japanese imports come to the UK via Ireland.
Before registration, non-EU cars under three years old must undergo the Single Vehicle Approval test (SVA) to prove they comply to European standards. The test costs £165, and covers a thorough inspection and testing for emissions, noise levels and safety standards. You may also have to convert speedometers from kilometres per hour to mph, uprate brakes, and fit rear foglights and side indicators where necessary.
