In my setup to set up DNS forwarding in the Vyatta router two steps needed to be followed. The first being configure an interface as a listen on interface. I configured this to be eth0 which is bridged to my Wifi rotuer. The second step is to configure a name server. I set this as the default gateway of the network i.e. the Address of the Wifi router.
Once done I was able to ping google from my vyatta VM.