Your company VPN will be hosted on an endpoint, like `vpn.yourcompany.com`
Can find out what that end point is? You might be able to find out by looking at the VPN client on the computer - there might be someone you can right click on the client to open a settings dialog which shows you the endpoint.
Once you know what it is, you can could see if it will respond to ping. Open up a terminal and do:
ping vpn.yourcompany.com
If that works, that's a good sign. It probably means that your IP is not blocked. If that doesn't work, it could mean either that your IP is blocked, or the end point is configured to filter/drop ping requests.
Are there any other people who work for your employer using the same VPN? Are any of them using Virgin Media? I have seen problems where hundreds of people have been unable to connect to a specific VPN end point because of peering problems between Virgin Media and a company's point of presence. It wasn't actually Virgin Media's fault, it was an issue with a peering provider between VM and said point of presence.