BT Cloud has some fairly basic functions to sharing images but I can find no way to directly link or embed BT Cloud hosted images into webpages (such as forum posts or Ebay). I suspect that this is by design with BT attempting to minimise bandwidth usage but it's a massive flaw for any sort of image hosting service.
I think you're right that BT have not enabled this feature on purpose (in fairness to them, they do advertise BT Cloud as a way to keep your stuff safe and share it with friends, rather than as an online image hosting service).
Having said that, I think I've found a (pretty convoluted) way of making this work:
Put the photos you want to share into an Album on BT Cloud.
On https://btcloud.bt.com, open the Album you just made, then click the 'Share icon' and then 'Share by public link'
Log out of BT Cloud, then open the 'public link' URL you just got in step 2
You'll now see the photos without being logged in.
Now, click on a photo so it goes to full-screen mode
Finally, right click on the photo (once in 'full-screen mode', and select 'copy image location' (this is what I clicked on in Firefox, other browsers might differ).
This gives you a URL which I am able to embed in other websites. I'm not sure if the URL will 'time out' after a while and stop working, or if it will be valid for as long as I have the photo album shared.
Good luck with it, and hope this helps. I suspect you may find services that are better suited for what you're looking to do.