The bank with my day-to-day account uses a Java applet for over-the-web account management, like paying bills, viewing online statements, etc. I often use it from behind a V.90 modem. It doesn't take any longer to load than most pages on the web. I also found another applet from the same bank used to query their share price. Also quite small.
Your HMO's applet is either far too large or their server was being very slow and very difficult. You should find an email address and tell 'em; they might be wondering why it's not very popular and have no idea why.
Wade.