Www.bbc.co.uk unreachable

What is the complete command that you are running, from what device, and what is the complete reply?

Edit - a note from review of your debug log - your DHCP server (the router) is passing out Google DNS instead of Pi-hole.

*** [ DIAGNOSING ]: Discovering active DHCP servers (takes 10 seconds)
   Scanning all your interfaces for DHCP servers
   Timeout: 10 seconds
   
   * Received 548 bytes from eth0:192.168.2.1
     Offered IP address: 192.168.2.186
     Server IP address: N/A
     Relay-agent IP address: N/A
     BOOTP server: (empty)
     BOOTP file: (empty)
     DHCP options:
      Message type: DHCPOFFER (2)
      server-identifier: 192.168.2.1
      lease-time: Infinite
      netmask: 255.255.255.0
      router: 192.168.2.1
      dns-server: 8.8.8.8
      dns-server: 8.8.4.4
      --- end of options ---
    
   * Received 548 bytes from eth0:192.168.2.1
     DHCPOFFER hardware address did not match our own - ignoring packet (not for us)
     DHCPREQUEST chaddr: dc:a6:32:a1:54:3b (our MAC address)
     DHCPOFFER   chaddr: dc:a6:32:a1:54:3c (response MAC address)
   * Received 548 bytes from wlan0:192.168.2.1
     DHCPOFFER hardware address did not match our own - ignoring packet (not for us)
     DHCPREQUEST chaddr: dc:a6:32:a1:54:3c (our MAC address)
     DHCPOFFER   chaddr: dc:a6:32:a1:54:3b (response MAC address)
   * Received 548 bytes from wlan0:192.168.2.1
     Offered IP address: 192.168.2.176
     Server IP address: N/A
     Relay-agent IP address: N/A
     BOOTP server: (empty)
     BOOTP file: (empty)
     DHCP options:
      Message type: DHCPOFFER (2)
      server-identifier: 192.168.2.1
      lease-time: 86400 ( 1d )
      netmask: 255.255.255.0
      router: 192.168.2.1
      dns-server: 8.8.8.8
      dns-server: 8.8.4.4
      --- end of options ---
    
   DHCP packets received on interface lo: 0
   DHCP packets received on interface eth0: 1
   DHCP packets received on interface wlan0: 1