Yes – You can easily apply for a new tax disc online
You will find your 16 digit reference number shown on your renewal reminder.
If you are applying for a new tax disc the DVLA will check whether your vehicle is insured and, if applicable has an electronic MOT Test Certificate/GVT Certificate or entitlement to disability exemption.
If you are also intending to take the vehicle off the road, declare Statutory Off Road Notification,( known as SORN) you can also do this over the internet.directly over the internet.
Update: Since this post was published in 2009 the tax disc has since been abolished. 🙁 Without this trusty reminder of the expiry date on your car windscreen you may forget the due date. Gone are the days when your renewal letter arrived in the post. So make sure have a reminder set up.