As per the many other threads on here, there is a known issue which O2 are investigating.
I have a solution!!
My problem was that I already have a Disney+ subscription, through O2, which I cancelled and restarted as they offers me another free period.
If, when you click the activation link, you get a blank screen that redirects to the Disney+ homepage then follow these steps:
This worked in Chrome for Android, YMMV
Click "activate here" in the "My Extras" section of MyO2.
The page will open and then redirect you. BEFORE it redirects you, click on the address bar of Chrome and copy the link. It should be a very long link with a lot of seemingly random letters and numbers.
Open an incognito window in Chrome and paste the address you just copied into the address bar.
Disney+ will load and prompt you to provide your email, do this.
It will then ask for your password, do this.
Then open the Disney+ app and sign in again if it asks.
Tadah! You are back into your Disney+ account with your O2 extra.