No internet access when VPN connected

Found it - The option is under "IPv4 Settings", "Routes", "Use this connection only for resources on its network".

VPN connection settings -> IPv4 Settings -> Routes

Check "Use this connection only for resources on its network".

Now if you can only access web sites but can't reach vpn network resources - you have to manually add routes to them (and maybe also check "Ignore automatically obtained routes")

For example I want to access resources on the vpn network with ips like 10.*.*.*, this configuration works for me:

Update for 18.04: gateway value is a must now, so enter "0.0.0.0"