I am trying to set up a guest Wifi which will be on a different VLAN on my network. I have got a Draytek 2860 with a UNIFI LR AP attached to port 4 of my router. I have configured the draytek as below.

Ports 1, 2, 3, 5 and 6 plus draytek SSID Native VLAN with no tag - network 192.168.0.0/24 with DHCP scope 192.168.0.100 to 150. All works fine with no issues.

Port 4 is on the native VLAJN and also VLAN 1 with a VLAN tag of 10 - Network 192.168.10.0/24 with a DHCP scope 192.168.10.10 to 50.

My AP is managed by the native VLAN and has a IP address of 192.168.0.40. This AP has the following setup:

SSID1- Normal user WIFI with no VLAN tag assigned. Can connect to it fine and surf the internet with full access to 192.168.0.0/24 network as needed.

SSID2- Guest account with network VLAN 10 assigned. Can connect WIFI to the SSID fine and ping the network (192.168.10.1) default gateway with no issues however cannot ping DNS or have any internet access.

It does not appear to be a firewall/filter issue and i dont want to allow layer 2 access between the VLANS.

I have a very similar setup using Vigor 2860ac with two Ubiquiti APs which work fine. Sounds like you may have a DNS issue with the second LAN which is used by the guest VLAN 10.
I would look at LAN >> General Setup and then click on the LAN which applies to your guest VLAN. Check you have "For NAT Usage" chosen and also the "DNS Server IP Address" are completed.

Also, on my Unifi controller I have the guest VLAN configured as "vlan-only" purpose with the vLAN tag entered. (Found in Settings >> Networks)