Council Tax
I suggest that you do notify the council immediately - they will issue you an invoice at the mulit-occupancy rate
KEEP THE INVOICE AND THE RECEIPT - this is important - then in two years time when you apply for ILR for your wife - you have proof positive that she has been staying with you at that address and for the full two year period
and by the way - it would be a good idea for you to Google SET (M) - then download the form and you will see all the requirements that you need to meet in two years time when she makes the visa application
you then know what to do now in preparation