Virgin are blocking connections to the SMTP port that do not come from their cable network. They appear to be accepting connections on the SMTP SSL port so you can try setting up your e-mail to use SSL (not TLS, SSL on port 465, the default port) and connecting that way.
The other alternative would be to open a free gmail account with google, configure your return or from address in gmail to be your normal virgin email address and using the google SMTP server to send mail.
Both of these solutions should work from both inside and outside the virgin cable network, but they might intercept SMTP connections from within the cable network and that could cause problems. If you always use a different port to 25, i.e. the SSL port 465 then there shouldn't be any issue and you can use the same setup to send from both outside and inside their cable network.
The first solution is better if it works.