A death in England should normally be registered within five working days, at the register office for the sub district where the death has occurred. It is done by appointment, and it takes around half an hour.
You will leave with the death certificate — buy several copies, as banks, insurers and pension providers each want their own — and the registrars certificate for burial or cremation, which we need before the funeral can go ahead. Ask about the Tell Us Once service while you are there: it notifies most government departments in one go.