App Store unable to install apps after upgrade to 11.0.1

I upgraded my iPhone 7 from iOS 10.3 to 11.0.1.

After that, all of the non-Apple apps cease to work, and (what is more important) no app at all can be installed through App Store app. When I request an app, App Store starts downloading it, but as soon as it reaches the 'installing' phase, it stops with a message 'Unable to Download App. <name of the app> could not be downloaded at this time'.

I 've had this problem for days, triyng a lot of things (checking the WiFi connection, reseting all settings , switching on and off the Apple store account, etc.). I went to a local App Store and was assisted by one of the employees there, without any success. I've called the Support Center: they don't now how to deal with it, and their only advice is to wait for the next iOS upgrade (i don't even consider the option of restarting as new the iPhone).

Help, please!