Cabinet Office hit by 1,000 in October alone
The government has fought off more than 6,500 digital attacks already this year, according to official figures.
The Cabinet Office was subject to 1,167 digital attacks last month alone, out of 5,857 during the course of the year.
But Cabinet Office minister Douglas Alexander said: "None of these resulted in compromise, loss or damage to any information held on the systems."
The Department for Environment, Food and Rural Affairs has detected 564 attacks so far this year, with 34 in October alone. It said: "These attacks were all stopped by our existing security measures."
The Ministry of Defence (MoD) said it was "subject to widespread and frequent attempts to probe its electronic boundaries", but would not comment on its anti-hacking policies on national security grounds.
It has suffered 10 hacking incidents, the MoD said, but "none of these had any significant impact on the conduct of military operations".
The figures were released in response to a series of questions by Labour MP for Milton Keynes North East Brian White, who is also chairman of public sector IT body the European Information Society Group (Eurim).
The Department for International Development claimed its systems had suffered just one digital attack, in October, when the Bugbear virus entered its system and infected 15 office PCs.
On two other occasions the department was hit by viruses Elkern and Redlof/A, but no hacking attempts were made.
Six virus attacks have affected The Lord Chancellor's Office during the year so far, but none caused damage to its IT systems.
The Department of Transport said the network it shares with the Office of the Deputy Prime Minister had been attacked 266 times in 2002 up to October. Eighteen of these attacks happened during October.
However, some departments seem to have remained beyond the electronic reach of hackers. The Department of Education and Skills, The Foreign and Commonwealth Office, and the Treasury all said there had been no attacks on their systems throughout the year.
The Treasury, however, did admit that one external website had been attacked while under construction.