I've got a reply from my webhost and this is what they say...

This could be because your IP has been banned (as for example we can visit your website without any problems). Please do one of the following to rectify the issue:

1. Wait 24 hours for the IP ban to go away.
2. Contact your ISP to change your IP for you.
3. Restart your router or modem which may change your IP. Please note that this may not change your IP and in this case you will have to choose another option.
4. Try to access your website by using online proxy service such as http://proxy.org/

An IP ban occurs when one IP address accesses server for more than 2000 times in 24 hours.

So I'm still really none-the-wiser. Any input from anyone regarding this issue would be appreciated.