Sorted it!
Give this ago if you're in the same situation. It seems that if there are no lists it only shows the 'Completed' list, which being completed doesn't allow you to add live reminders to it.
I clicked on the list icon (top left) and seached for something - nothing found, but then an edit button appeared which let me create a new list.
Once you have a list in addition to the completed list, they appear in the main app with the + icon.
All seems to be fine now.
BTW - I had my old mac/me.com account in the Mail, Contacts, Calendars settings along with the new iCloud details, I decided to delete the old mac/me.com from here leaving only the iCloud as it was duplicate infomation - this might have had an effect too - not sure, but as it's gone now no way too check.