Some account services will not be available until you sign in again

This is driving me crazy. It started with my phone but now is an issue on ALL my devices - Ipad, Iphone and IMac. I'm getting this notification 'some account services will not be available until you sign in again'. I have logged out of icloud on all devices and then signed in again. This has done absolutely nothing!

Also, my phone keeps asking for my apple password and blocks me accessing any apps on the phone until the password has been entered (usually have to enter it twice). As I use lastpass I can't access my password which effectively blocks me from my phone until I can get home and look up the password on another device.

Is this an apple bug? Or is there something wrong with something I am doing? Any advice would be appreciated as I am about to throw the who apple kit and caboodle out the window. Thanks.