I also have this issue, exactly the same as the OP describes it. I was on chat last night with apple tech support for nearly 2 hours trying numerous things. The tech rep said that signing out of iCloud on the phone and back in was the last resort, because ofc it unsyncs everything and then has to sync it back again. I didn't do that step because I didn't want to risk the phone potentially not being able to sign back in and then god knows what state the phone would be left in.
But I did try resetting the network settings, uninstalling my VPN, signing out of iCloud on an old iPad and signing back in, signing out of iCloud on my Windows laptop and signing back in. After each sign out I would try and accept the new T&Cs on my iPhone, then reboot and trying accepting again, then signing back in on the device etc. etc. following the same pattern. So I tried every combination I could think of trying to accept terms on another device but you just don't seem to get the option, you can just sign in and out. I also signed out of purchases and then tried downloading a free app to force me to sign back in, back that didn't work either.
Thing is I've lost my recent phone history I'm sure because of this as it's not being synced with iCloud, and I think Whatsapp does it's backups to iCloud if I remember right. So at the moment I, and presumably everyone else, in the same position has just lost access to whatever gets synced to iCloud. Also I pay for a bit of extra storage, not a lot - just the 99p option for 50GB, so technically I'm paying for something I can't get access to.
I note that English_in_Berlin above said the matter is being looked into and a solution should be forthcoming soon, but that's not what I was told by tech support. They told me that Apple are aware of the issue and it is being looked into, but it's not definite they will provide a bug fix for older phones. His exact words were "they *may* provide a fix if they feel it is necessary", which doesn't exactly inspire confidence. I think that if not enough people complain about the issue on older versions of iOS then they just won't bother.