The Council Tax, along with all other household bills, can be paid for in the normal fashion whether monthly, quarterly or whatever so I would not worry too much re that side of things although it is true that if you wish to sign up for a new mobile phone contract you may have difficulty in doing so.
The timescale depends on a number of factors, but after choosing your provider (go to
www.iva.com have a look round there re reviews etc, making sure you talk to 2 or 3 providers) you will be sent a proposal in writing. From there, assuming no problems etc, the typical timescale is between 6 to 8 weeks, but that can of course vary from case to case depending on the details of the case.
Hope this helps.
Regards.