I thought CT was not payable on an uninahbitable property
see and start at
https://www.gov.uk/government/publications/council-tax-domestic-properties-in-disrepair-or-derelict
I havent read the document - if it has a working bog a dwelling unit is usually habitable - the rules are likely to strict
otherwise within a week or two - they dont worry so long as the CT line is continuous - that is they dont miss out on CT from the gap ....
I do this on the day the tenant moves in as companies and council are so likely to double charge and then say "oops!"
recenlty I had accounts for the same property for me, the new occupier and the named tenant - triple CT - great work if you can get it.