6 months is a ball part figure as it could take that long depending on if the application is straight forward.
Also take into account any Bank holidays.
This is a Time line for my families application.
Processed Application through NCS on 17 Dec 12
Money taken 04 Jan 13
Letter of acknowledgment dated 4 Jan 13
applications processed 25 Jan 13
Citizenship Ceremony 10 Apr 13
British Passports issued 28 May 13
Hope this helps