Hello @discomatt,
Thanks for writing to us.
I checked your site, It seems that the URLs are not fully replaced while moving the site and that is causing the issue to load the images in the media and frontend.
Please have a look at the given screenshot below.
I would suggest you contact your hosting provider to correct the URL.
OR
You can also try out this arcticle on how to update the URLs when you are moving the sites.
I would also recommend you to provide the proper permission of the Uploads directory that is available in the wp-content/uploads. To add the permission on uploads directory you can access it by using FTP or Cpanel.
Also, remember that the exact URL should be mentioned in Setting > General , WordPress Address and Site URL , including the protocol i.e HTTP/HTTPS.
Hope this helps.
Thanks