Good news! Overnight I have updated our database to replace all PhotoBucket image links to the new image hosting location and everything seems to have moved over as expected. All images should now appear again as they should, the standard PhotoBucket "ransom image" should have disappeared and the all images are lots quicker to load as well
Whilst all images (in posts, not in signatures etc) that were previously hosted on PhotoBucket have now moved over, I have left any links to PhotoBucket albums etc. in place. These links will continue to work fine and I didn't want to lose this if someone has deliberately linked to an album.
As mentioned in my original post, you may continue to use PhotoBucket if you wish, but we strongly recommend that you use another provider for now. I'm in the process of making posting images on the forum a bit easier - more on that later!