You are the policy holder, the policy will tell you which car is insurred.

When you swap cars simply go on-line, phone or pay a visit if its a local broker and give them the details of the new car. They will then probably ask for some extra money. Once paid your existing policy will transfer to the new car at an agreed time and will run until the renewal date. At renewal proving you have had no incidents you should get the extra years no-claims (providing you are not already at max NCB).

The buyer of your old car will obviously need to insure it in their name if you sell it privately.

Dont forget about the continuous insurance rules, if you buy the replacement car before selling the old one you will need to ensure its still insurred unless you have sent the tax disc back and SORN'd the car.

Simples.

Usually your insurer will amend the details of your existing policy so the policy covers the new car. You'll normally pay an admin fee for this service plus any difference in the premium on a pro rata basis. The only time this might be a problem is if the new vehicle is of a much higher insurance group on the existing car and they are unwilling to cover you for that vehicle.You'll then receive a renewal notice at the end of the year as normal-then you get to use your NCD.

Your policy won't become 'invalid' when you sell the car since you do not need to be the registered keeper to be insured to drive it. You would still want to inform your insurer/broker just in case the new owner gets involved in an incident.