If you tax in the last few days of the month, there is now an exemption from the offence of not displaying a tax disc. This exemption covers the first five working days of the month and allows time for the new disc to arrive in the post.

The exemption only applies if applications are made before the current tax disc or SORN expires.

You get a confirmation email immediately after renewing online so it wouldn't hurt to keep a printed copy in the car. Not proof I know, but it might help a bit if pulled over.