Solution: The simplest way to solve this is to add the VPN Client service executable (vpnagent.exe) in the Trusted Zone.
To do this, open Kaspersky and click Settings.
Click Trusted Zone
Select the Trusted Applications tab and click Add.
Click Browse -> Applications and choose vpnagent.exe from the list
Check Do not scan network traffic. Do not scan opened files does not have to be checked.
OK OK Apply OK and that's all. AnyConnect should now be able to connect to the VPN.