You can 'phone the Pension Service on 0845 6060265 to report the death. If you tell the Registrar there was benefit in payment, you'll get a form called a BD8. The DWP will accept the BD8 as verification of the date of death but they will also be notified by the Registrar. On the back of the form there are a fair few questions about the deceased and it also asks who is claiming the arrears. Another form called a BR330(LO) is used by the DWP and the person claiming the arrears fills it in and says what the basis of the claim is, executor, paying the funeral costs for example.