Having probably queued to get into Britain, thousands of overseas residents, including senior business people and academics, now face the prospect of being unable to leave the country, possibly for weeks, because a key UK border agency computer system has crashed.

Hundreds of people queueing at UKBA's public inquiry office in Croydon, applying to extend or renew biometric residence permits, were told to go home on Thursday because the computer system could not cope.

The details of more than 600,000 foreign nationals living in Britain have been logged on the biometric residents' identity card database since it was set up four years ago.

But it has suffered repeated failures in recent weeks which culminated in a complete breakdown on Thursday. All afternoon appointments have now been cancelled for the next two weeks.

"It seems quite incredible that UKBA can arbitrarily cancel people's appointments, send people an email claiming that people have cancelled their own appointments, and then offer absolutely no alternative other than to rebook at a much later date for an appointment at the other end of the country," said one applicant in an email to the Guardian after having an appointment cancelled.

Immigration lawyers, including those representing overseas investors and entrepreneurs, said that all alternative appointments were booked for at least the next three weeks. The only other option open to applicants was to apply by post and send in their passport to obtain a new visa, but that risked being unable to travel for months while the application was dealt with.

Maria Patsalos of Mishcon de Reya said: "It's just madness at the moment. We have had chief executives caught up in this who can't understand why it is so backward. It's also affecting major investors. There are big problems with the computer system which crashes continually. These are often high net worth people who need to be able to travel. It is a complete mess that is getting worse."

Among those whose appointments were cancelled were foreign nationals who had paid £1,326 for a 24-hour visa service that enables them to keep their passport so they can continue to travel.

A UK Border Agency spokesman said they were experiencing some IT problems in their Croydon public enquiry office that they were working to resolve as quickly as possible: "In order to complete cases that have been affected, we will be reducing the number of daily appointments until 18 May. We will prioritise completing all outstanding applications and those with cancelled appointments can rebook through the UKBA website or can submit postal applications using our postal service."

But Keith Vaz, the Commons home affairs committee chairman, said it was a shambles and another example of UKBA's failure to plan properly for a new scheme.