There is nothing stopping you subscribing to Disney+ and Paramount+ and having the apps on a Fire TV stick or Roku stick.
You can subscribe to Paramount+ on a BT TV box indirectly through Amazon Prime Video.
No Disney+ unfortunately, although many newer TV’s now have the app.
Best to get an Amazon Firestick and get Disney + and Paramount + there.
If you still want some Sky channels then also get Now(Now TV) direct with discounts.
As yet dont have Paramount + but do have Disney + and Disney + has become one of my most used apps.
I cancelled BT TV about 9 months ago.
In the last 14 to 18 months I now use the Amazon Firesticks more than I do my Youview box for apps.
Also to note the new ITVX has so far not arrived on the Youview box but is on the Amazon Firestick and the Ruku.
There seems to be something 'strange' going on with ITVX. I'll put my findings in the ITVX thread.