The Home Office and Downing Street websites were hit by distributed denial of service (DDoS) attacks by supporters of the Anonymous hackers collective on Saturday night and Easter Sunday.
Supporters were urged to join the assault via messages on Twitter.
DDoS are difficult to defend against because thousands of separate computers are used to flood websites with requests simultaneously, overloading the servers.
The hackers collective, which announced the attacks in advance but was still able to mount them successfully, has vowed to bring government websites to a standstill every Saturday. "Told you #toExpectUs!" said a message on the group's Twitter feed.
The group said the attacks were in protest against the government's "draconian" surveillance proposals, and also the UK's extradition treaty with the US.
Among the extradition cases in the spotlight is that of Gary McKinnon, the British hacker who suffers from Asperger Syndrome and who supporters believe should either be freed or tried in the UK.
The apparent ease of the attacks – and the promise of more to come – must call into question the government's ability to cope with common security threats.
But Whitehall is not alone: just in the past week, Anonymous has hit the Vatican, and a number of websites in China in protest against censorship.
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