All vehicles must either have a valid tax disc or be subject to SORN (Statutory Off Road Notification). At the moment that the ownership of a 'SORN' vehicle is transferred, the SORN is automatically cancelled and the new owner is obliged to either tax the vehicle or (if it's to remain 'off road') to re-register SORN.
You can't drive the vehicle until you've got a tax disc. For that you require a certificate of insurance (or a cover note). If you insure online, or by phone, you'll have to wait until you've got documentary proof of your insurance cover before you can tax (and drive) the vehicle. If you insure via a local broker, you can get a cover note straight away, which will enable you to tax (and drive) the vehicle on the same day that you purchase it.
Chris