Transfer dates

Ian - the register is deemed to have been updated from the date the application was received, so that's the registered on date you will see on the register itself.
The other date to consider is the completion date, namely the date of your Transfer itself as that is the date when you are in effect the new owner. 
I would check with the council as to when you are deemed liable for council tax 

Ian - how re register applications has been the same re dates for decades. The issue appears to be which date the council then uses to assess any payments due for their own purposes. We have no say in their processes so worth speaking to the council to clarify as I've never come across similar issues raised re such matters before. So something appears awry and hopefully the council can review and remedy that for you.