Go to Internet Options while logged into that account. Security, Custom Level, Downloads, File Download, Disable.
Then, you would want to disable access to the Internet Options. This can be done in Home with this "security console":
http://www.dougknox.com/xp/utils/xp_securityconsole.htm
The unregistered version doesn't allow you to log on to other accounts, so you would need to use it from within that account and then hide the program itself.
With the registered version, you can log on to other accounts and adjust the settings for each account from any Admin account.
This gives some of the Group Policy functionality to Home Edition.