After someone passes away, their death must be registered with the Births and Deaths General Register Office - contact details of the Deaths Registry can be found in useful contact.
The Deaths Registry will give you a 'certified copy of a death entry', more commonly known as the Death Certificate. Most organisations, including HSBC, will need to see original documents and so you may want to arrange for extra copies of the Death Certificate from the Deaths Registry – these additional copies are available at a charge.
This is step 1 of 5 outlined on the overview page
Bereavement Guide - you may save an electronic copy of the Bereavement Guide. Alternatively, you may print out the Bereavement Guide.