I assume that you have a smoothwall firewall. But, I'm confused by what you mean.
Is your computer connected to the internet, or do you go through a gateway/firewall?
If it is the latter, you may not be able to connect to your work computer from home, unless the firewall is configured to forward the VNC ports to your work computer's IP address. Connecting to your home computer from work may be possible if your companies firewall will allow the ports through. A NAT router will notice the LAN IP that is initiating a connection. Then it knows which LAN address a returning packet is for. If you try to connect from home, it has no way of knowing which LAN host the connection is for. Initial VNC ports can be forward to a single host, but only one, unless both sides of the connection are configured to use nonstandard ports, and the router knows which port is assigned to which LAN host.
If your work computer has an internet IP address, or does static nat translation then it may be possible to connect to your work computer from home. For example, you may have an internet address like 18.104.22.168, that the firewall translates to a lan address of 10.0.1.100. You could be registered with a DNS address such as kesp.companyname.com. All allowed ports on 22.214.171.124 from the internet are forwarded to 10.0.1.100.