You chaps are right. No dedicated IP. That makes sense now I think about it. So I'd have to go down your route the_winch of using the alternate URL, except I don't think my hosting company provides one. I'm with Hostroute/Myqth. I can't find examples or documentation/help explaining how I'd link to it any other way than with a registered domain that they'd set up. Hmmmm.
All is not lost. I can get free low-speed hosting, as a guy I live with runs a file server from our house. So upload won't be great, but it'll still work. Alternatively, I could buy another package. I just don't see the point in paying for a domain anymore when all I use it for is hotlinking URLs which I post on other boards.
Thanks for your help though chaps. I'll have a think about what to do. Meanwhile, there will be A LOT of dead links about for all my stuff!