To use openconnect in Ubuntu 15.10 you have to set a default route to the tun0 device that is opened up. Otherwise no traffic will be routed through the tunnel. To do so:
sudo openconnect https://yourvpn.com
wait until the connect banner passes and openconnect displays:
Connected tun0 as ##.###.###.##, using SSL
Then open a new tab on the console or put openconnect in the background. Enter
sudo route add default gw ##.###.###.## tun0
This will route all outgoing traffic to the default gateway which is your tunnel.
Theres a bug opened up in ubuntu launchpad. While it is being investigated/fixed you can use above hack to still use VPN with openconnect.
Bug: network-manager-openconnect / 1502847
Via: openconnect-vpn-setup-is-failing-in-ubuntu-15-10