The problems are now all sorted, according to sources. This can also be verified by the Playstation Network status page, which can be found here.
All core PlayStation Network services, except the PlayStation Vue TV streaming service, were suffering from issues, according to the PlayStation Network status page. The affected platforms include all the major ones: PlayStation 4, PlayStation 3, and PlayStation Vita.
We're aware that some users are experiencing issues logging into PSN. Thanks for your patience as we investigate: https://t.co/m4NXhLzkQQ
— Ask PlayStation UK (@AskPS_UK) October 26, 2016
There was scheduled maintenance on the PSN overnight, but this appears to be a separate issue. The Ask PlayStation UK Twitter account acknowledged the problems in a tweet today, saying it's aware of people having problems logging into the network. "Thanks for your patience as we investigate," it said.
This is the second straight week that PSN has encountered some problems, as Sony acknowledged last week that some users were unable to sign in to the network.
As usual, your mileage may vary. We'll update this story as more details become available.