Executors of a will take their authority from the will, and probate is confirmation of that authority. They are able to take up their duties from the moment of death. Where the estate is very small, they may be able to close bank accounts without formally obtaining a grant.
In contrast, administrators take their authority from the Grant of Letters of Administration.
The first step is to notify all the interested parties that the death has occurred. Banks and building societies, company registrars and so on should be written to with the death certificate and a note of the date of death.
Please note that it is no longer acceptable to photocopy death certificates. They are crown copyright. Professional practitioners have entered into a protocol with the banks, etc., whereby they send a death notification form containing the details copied from the death certificate. Lay executors administering estates in person will need to purchase extra copies of the death certificate.