I would try either
squid and turn off the cache function (it's in the configuration HOW-TO guide) or you could use iptables to block outbound http traffic that is coming through your gateway router.
Squid can be a little bit of a challenge to setup at first, but is excellent for higher traffic situations.
To use iptables, you would have to add a rule to block outbound http packets that are not destined for
www.bank.com. The exact rule would depend on how your network is setup, but would look basically like this:
iptables -I FORWARD -p tcp --dport 80 -i
internal_interface -o
external_interface -d !
ip_address_of_bank.com -j REJECT
Savy users will be able to get around that rather easily. A more effective way to do it (but more complex as well) is to use iptables and squid in combination. You would block all port 80 traffic and then setup squid to listen on some higher port, then configure each of the clients to use the higher level port of the proxy server for communication.