Reports on the DownDetector website indicate that subscribers in the UK, Ireland, Greece, Italy, Portugal and Germany are among those affected.
The problem appears to have begun after 14:00BST.
Some affected users have, however, reported that issues with email and other internet-based activities have been resolved.
The fault comes a day after the firm announced that it had begun allowing users to link their accounts to Amazon’s Alexa service, letting them call contacts via the US company’s smart speakers. However, there is no suggestion that this was the cause of the outage.