Good thought to clear the cookies, but sadly didn't work for me. Same problem 😞
Have you tried another browser?
I've not used the BT cloud for some time as I think it's badly implemented (believe me, that's a very reserved opinion) but I've tried it a couple of times today and managed to sign in OK each time.
I still suspect it could be related to closing the browser down without signing out first, but if clearing cookies doesn't prove it then I can only suggest trying another browser, preferably one that you haven't used to access this site before.
I normally use chrome so tried using ms edge still no luck also cannot access on tablet android app or phone android app. not sure if its related but all seemed to start at beginning of week when bt decided to move me from bt/yahoo mail to bt mail, next day and ever since had problems with log in to mail intermittently and no access to cloud.
Cloud dashboard says I am using 0.0 B (100%) of 0.0 b at one point this afternoon the dash came up as normal showing 1tb of storage for a few seconds then went off again. You would think that as the problem is on two separate computers and 2 android devices that the common denominator must be BT I will try to phone tomorrow but dont hold up much hope in the current situation.
I have now tried using Chrome, Safari and Firefox on both Mac Catalina, iPad running iOS 13.5, Huawei P20 Pro using the latest Android and none of them work. I have cleared all cookies, disabled all plugins and extensions and it still doesn't work.
This is definitely a problem on BT's end.
Logon to MyBT, click Manage Your Products and then click on BT cloud, what does it say your Current Storage Limit and Current Usage are?
went to my products, cloud, manage it says I am using 80.1gb of max 1000GB which is what the dash showed for around 30 seconds this afternoon.
As I said in my original message, I have tried different browsers. The problem appears to be with the server.
It's definitely an odd one but I think there would be many more people posting if it was a BT problem, I can only suggest that you take the advice of @DavidM in message 7