to the forum.
You created this thread in our Articles sections, which would have prevented anyone answering it. I have moved it to the correct forum for you.
As for your question. You will have to use a router. It can be a either a dedicated router (if you don't want wireless, you can disable that part) or an old PC with Internet Connection Sharing enabled.
The problem is that every device attached to the Internet needs an IP. Virgin Media will only provide ONE per account on their residential service. A router will be able to issue it's own IPs and manage communication between the internal network and external internet. A switch will not.
The other option (if you really don't want a router and don't mind rebooting the modem everytime you switch to the other computer), is to reboot the modem everytime you switch.