The DVD writing laser in my Sony DVD RW DW-U10A in my Apple iMac (Flat
Panel 1GHz 17", 2003) has apparently failed. (a) How can I test this
to make sure I'm correct in my diagnosis? (b) What model should I
order and from which retailer? (I live in the UK.)

Call Apple.  I don't know the number in the UK.  Your computer doesn't
have to still be under warrantee.  They'll walk you through what you
need to do.