The first day of the paperless car tax system has descended into chaos with the Driver and Vehicle Licensing Agency (DVLA) website buckling under "unprecedented demand" for the electronic version of the disc.

From today, vehicle owners will no longer have to display the vehicle excise duty (VED) disc on their screens, with those needing to renew their VED either doing it online at the DVLA's car tax website or at Post Office branches.

But many people have been unable to get on to the DVLA site, prompting the agency to issue an apology and to advise vehicle owners to "keep trying".

The AA reported that a number of its members had complained about not being able to access the DVLA site, with president Edmund King saying it was "a bit ironic in this digital age" that the system had been overwhelmed.

The DVLA said: "More than 270,000 people successfully used our online car tax service yesterday - that's 30,000 more than on the same day last year.

"We are currently experiencing unprecedented demand which means that some customers may be experiencing slow response times or having difficulty accessing the service.

"We are of course very sorry for any inconvenience and we are urgently investigating to improve service quality for the minority of our customers that are experiencing issues."

A DVLA spokeswoman said: "The system has not crashed - it's just slow at the moment. We are advising people to keep trying."

Earlier this year, in written evidence to the House of Commons Transport Committee, the AA said: "The AA believes that ailing mainframe systems like the vehicle and driver registers at DVLA have worked admirably well given what is now expected of them.

"However, they are no longer fit for purpose to deliver the motoring agencies' vision now proposed."

Today, Mr King said: "We've had a number of our members coming on to us say that the DVLA car-tax site has crashed. It's a bit ironic in this digital age that the site goes down on the first day of the electronic system coming into being.

"I think that not only a lot of people have tried to get on to the site to renew their car tax but also a number have tried to access the site to find out how the changes to the car tax system affect them."

Bob Dowson, director of the website performance division of global information assurance firm NCC Group, said: "Of all websites that experience peaks in traffic, the DVLA should have had a very good idea of the number of renewals to expect and should have prepared accordingly.

"It is relatively simple to load test a website in order to ensure it can withstand an increase in visitor numbers. However, in this case it seems the DVLA either underestimated the surge in traffic or failed to test the site properly, resulting in downtime and sluggish loading."