Make sure you are subject to the tax:
http://www.northampton.gov.uk/info/200028/council-tax/1003/council-tax-what-to-do-in-the-event-of-a-death
When a property had been occupied by a single person, who either owned or rented the property. and that person dies, the property is exempt from council tax payment for as long as it remains unoccupied, and until probate is granted.
Following a grant of probate, a further six months exemption is possible as long as the property remain unoccupied and has not been sold or transferred to someone else.
It is important that the executor(s) keep the council tax office informed of:
the date probate is granted,
details of the transfer or sale of the property or the end date of the tenancy,
when the estate is settled