I noticed that I have, as expected a dedicated IP address from my ISP, but that the internal IP range of the ADSL router was set to 192.168.0.x range.
Surely this is wrong, and it should be set to the same range as my Air Port Express units shouldn't it, and if so I am not quite sure how the network has worked all this time.
In your current network configuration, you have two routers in series, each with their DHCP server service enabled. Most non-Apple routers typically provide DHCP clients with IP addresses in the 192.168.n.n range and is exactly what your current ADSL router is doing.
Since you have the first AirPort Express Base Station (AX) directly connected to this ADSL router, it will receive an IP address on its WAN port in this 192.1689.n.n range, but since it too has DHCP server service active, any wireless clients connected to it would receive IP address in the 10.0.n.n range.
You would also have a "double NAT" condition. In itself this is not necessarily a bad thing, but does tend to introduce other issues, especially if you wish to share resources between clients connected to either router. In most cases, where you have routers in series, you would want to reconfigure the downstream router as a bridge.
I would suggest just reconfiguring the AX as a bridge. If you prefer that network clients are provided IP addresses in the 10.0.n.n range, you can just adjust the DHCP server service in the ADSL router to do so.
To configure the AX as a bridge: AirPort Utility > Select the AX > Manual Setup > Internet > Internet Connection tab > Connection Sharing = Off (Bridge Mode)