As a follow-up, I understand the lack of an online searchable database for Birmingham as a whole is the sheer size of the task. Taking Handsworth, B'ham as an example the database would have to cover 3 crematoria and 11 cemeteries, some of which go back to 1836. They report almost 70,000 burials since 1909.
An alternative to the NBI CD-ROM is microfilm/microfiche copies of the burial index's at Birmingham Central Library since the NBI may not be complete.
As an aside, for those with general West Midland interests, I would like to highlight Dudley Metropolitan Council's online searchable index for burials and cremations, which is not only useful for single enquiries but for one-name researchers such as myself.
Regards,
Mark