"Webspace" is essentially a website.
In the past Internet Service Providers would give you free webspace, but very few people actually wanted to create their own website so now most, if not all, ISP's have discontinued their webspace service (BT got rid of their years ago and Virgin a year or two back, I don't think Plusnet ever had it).
You can still get webspace of course and, as mentioned above, you'll then have complete freedom to upload and link to images on it. But it won't be free:
Top 10 Web Hosting Companies (You could set up a home webserver but that would be a bit excessive just to post images to a forum).
~iw