Car insurance and road tax go hand in hand. In the UK having current, valid insurance and road tax for your car, motorbike, van, etc if it's used or parked on the road, is a legal requirement.
You have to prove your vehicle is insured before you can tax it, whether you're doing that at the Post Office, by phone, post or online.
If you're taxing your vehicle online or by phone, your car insurance is automatically checked on the Motor Insurance Database. If your vehicle is more than three years old and should have an MOT certificate, that's checked automatically too. If you're applying for road tax by post or at the Post Office, you'll need your current Certificate of Insurance to prove you have valid insurance for the period when the new tax disc starts (and your current MOT certificate too).
You'll still need to do this if you have a Historic vehicle (one that was first registered before 1st January 1973) or any other vehicle that's exempt from making a payment for tax. Although you don't have to pay for the tax disc, you still have to display it in the windscreen, so you'll still need valid insurance and (where its appropriate for the vehicle), a current MOT certificate.
What if my car is off the road?
If your vehicle is off the road (perhaps for major repairs or because you don't use it during the winter) you can save on the road tax by declaring it SORN (Statutory Off Road Notification). The vehicle has to be genuinely off the road (i.e. not just parked on the street in front of your house). You're not legally obliged to insure it either, but bear in mind that if anything happens to it while it's uninsured, such as catching fire or being stolen, you won't be able to claim.