The other thing to remember is that new rules came into force in 2014, saying road tax was not transferrable between owners of a car. So, before you can drive away the car you’ve just bought, you need to tax it. This might seem like a long time ago, but most people won't have bought their next car since 2014!
If you’re buying from a dealer, they will be able to sort that for you. However, if you’re buying the car from a private individual, you can’t take advantage of any tax that’s left on the car.
To tax the car, you need the new keeper section of the V5C online – another reason to insist on seeing the V5C before you buy the car – and you can tax the car immediately, either online via gov.uk, over the phone 24-hours-a-day, or at a Post Office that deals with vehicle tax.