Thousands of customers have been unable to renew their car tax online, after the Driver and Vehicle Licensing Agency (DVLA) website was swamped.
A new system comes into operation on Wednesday, after which it will no longer be necessary to display a paper tax disc in the windscreen.
But some motorists have spent up to 13 hours online, trying to get their car tax renewed.
The DVLA said the site had seen "an unprecedented volume of traffic".
Mike Dewsbury from Manchester was one of those who struggled to pay for his car tax - known officially as Vehicle Excise Duty (VED).
"It's a joke. I need to get to work but legally can't because my car isn't now taxed," he told the BBC.
The DVLA said that an extra 30,000 people had visited the site, compared to the same day last year.
It apologised for the disruption, and advised people who need to renew their tax urgently to do so at a Post Office instead.
Meanwhile the AA has complained that the new vehicle tax system will provide the government with extra revenue, as some cars will, in effect, be taxed twice.
Under the new tax disc system, someone buying a car will no longer be able to benefit from any unused period on the disc.
But while buyers will need to renew the tax immediately, sellers are not allowed a refund for just part of a month.
So if a car is sold on say, the first day of the month, both buyer and seller will have paid the tax for that month.
"Someone driving a car that costs £500 a year to tax would lose £41 if they sold it at the beginning of the month," said Edmund King, the AA's president.
"Likewise a buyer purchasing a car mid month would have to pay Vehicle Excise Duty for the entire month," he added.
However the DVLA said it would not bring in much additional revenue.
It said it was always the case that car-sellers were only credited for each whole month that the disc was not used.
And it added that 65% of cars bought do not include tax passed on by the previous owner.
The RAC has previously said the new system will result in tax evasion to the tune of £167m a year.
But the DVLA dismissed that claim as nonsense.
It said it expects to save £10m a year by not having to print and distribute paper tax discs.
Those who have not paid the tax will be spotted on number-plate recognition cameras, or their details will show up online.
Other changes coming into force on 1 October include a higher national minimum wage, and new rules on people who die intestate.