The UK’s County Council in Lincolnshire refused to give in to a ransom demand of just £350 and immediately found its computer systems in a lock-down which lasted nearly one week.
The demand was for an initial $500 in the digital currency Bitcoin but that amount would increase over time if not paid.
The threat was made using ransomware through which data is encrypted and unscrambled only if the victim pays up.
Ransomware has been described as a virus which locks a device such as a computer, tablet or smart phone and then demands a ransom to unlock it.
For Lincolnshire Council, the attack was triggered last Tuesday when a specific email was opened. Usually, the virus is contained in an attachment to an email which appears to be innocent.
Once the attachment is opened it freezes the machine making it impossible to access or store anything on the computer.
Ransomware came out of the US in 2005 and spread to other parts of the world since then along with other malware.
Judith Hetherington-Smith, from the council, said that since the attack, council staff had been making "lots of phone calls", having "lots of human contact" and making use of pen and paper.
The Council is hoping that the computer systems will be back to normal on Monday after scanning all its data and security measures to “make sure it’s clean”.
Lincolnshire Police are trying to identify who is behind the attack.