Hi Neil,
Blocking an IP address has nothing to do with Zen Cart itself. It's more of a server setting.
Considering that, I'm a bit surprised at Fasthost's rather misleading (and succinct) response.
When they said that you "couldn't do it on the server", I'm not sure what exactly they meant by that. Perhaps they meant you can't block an IP address using your web control panel. If so, that's not unusual. My host uses "Parallels Pro" and that (as far as I'm aware) doesn't have an IP blocking feature. Instead, I have to use the .htaccess method which Mary linked to. For that method, you would have to use an FTP programme such as FileZilla (client). This would connect you to your site's files on your server where you would have to either edit or create what's called a ".htaccess" file and enter into it some code similar to that from the link earlier. FTP is an easy-to-learn and common task which I think the majority of users here know how to do. So it's worth spending a bit of time with it.
Firstly, do you know whether you're on a Windows (iis) server or a Linux server? Also, what is your web control panel just in case you can actually use it for this?
(Ultimately this is a server issue and so your host should be helping you with this)