I've managed to set my IP address, it seems as though you can have any IP address within the Class B or C ranges defined by liquorice earlier:
Thank you to everyone for helping.
Please can anyone confirm or correct my understanding of public and private IP addresses?
If BT choose to set their own classes and limit the choice of private IP addresses, that's fine, I'm sure they have a perfectly coherent business case for it.
Am I correct in thinking that in theory a private IP address can be anything within the limitations of IPV4?
No, the address ranges I listed are the only ones that are designated as private addresses and are not routable on the internet.
after much faffing around and a number of useless call to BT I managed to find the answer.
Once you change the local IP address you need to update the DHCP settings - I suspect you already tried this (like me) and found it can't be changed either. Bad UI design if you ask me as it's not obvious how this setting works!
Basically, the trick is to select 'Custom' in the DHCP options list. This will allow you to change the DHCP address range to one that matches you new IP. Now, when you click 'Save' the new settings will be applied. It seems that if the DHCP address range is unchanged the settings are not saved (for good reason).
Hope that helps.