Just to update on this, the offer of free lookups is still valid.
I sent off a form yesterday to ask if they could check the Newcastle Evening Chronicle for a 1909 death notice.
Always a chance there wasn't one, but the current newspapers online only have Jan - Jun for this year and the burial I had found was in Sept.
Got a reply (complete with a scan of the entry) this afternoon.
Really grateful for this service, especially at my favourite price of free :-)
Full marks to the Library staff !
Boo