@ScottGK 

I have the exact same config. a dns that points to a singel local dns server. I only get one DNS server, which type router do you have? and what does the ip config say about the dhcp server, is it the same ip as the router?

  @MR.S 

Router is a TP-Link ER706W ip: 172.20.8.1

IP Config shows DCHP correctly as 172.20.8.1

Turns out I'm also having problems with some clients accessing the internet even though their settings are correct.

Only difference in the original router (a Dlink DSR-1000AC) which I'm replacing with this one is that on the Dlink router I was able to set the DNS Server on the WAN port to our internal DNS server. The TP-Link won't let me do that. Not that it should make any different because the clients should only be pulling from the network DNS server.

  @ScottGK 

I thought it seemed very strange, the dhcp server should not give out more dns servers than you have specified in the dhcp server. Does this apply to all clients or is it only on a single pc?