The Guardian said the website was hit by a "sophisticated and deliberate hack" which has affected a minority of the 10 million unique users the site gets per year.
The company is not releasing technical details because the incident is being investigated by New Scotland Yard's central e-crime unit.
On Saturday The Guardian emailed around 500,000 users whose information could have been compromised, advising them to contact creditors and credit reference agencies and consider subscribing to UK fraud prevention service Cifas.
The email said the data that hackers have got hold of could include users' names, email addresses, covering letters and CVs, but is not believed to include any financial or bank data.
The Guardian's US jobs site was not affected.
Digital
Hackers hit Guardian Jobs website
LONDON - Hackers who targeted The Guardian's UK jobs website on Friday night may have got hold of CVs for up to 500,000 users.