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Websites for the Guardian, Financial Times, Independent, and the New York Times were among those down.
The UK Government website - gov.uk - was also not working, giving the error message "Error 503 Service Unavailable".
Several websites affected by a major outage are reporting that the issue is linked to Fastly, a cloud computing services provider.
The Guardian tweeted: "The Guardian's website and app are currently being affected by a wider internet outage and will be back as soon as possible"
Alex Hern, the Guardian's technology editor, tweeted that Fastly "has been identified as the cause of the problem".
"The outage, which began shortly before 11am UK time, saw visitors to a vast array of sites receive error messages including 'Error 503 Service Unavailable' and a terse 'connection failure'," he tweeted.
The Quartz site has also attributed the issue to Fastly via Twitter.
Other websites affected included the online discussion platform Reddit, the Evening Standard and French newspaper Le Monde.
Service monitoring website Down Detector registered a spike in reports of outages of Amazon's cloud computing platform Amazon Web Services.
As of 11am on Tuesday, the site recorded 1,700 reports.