As Uptoncx said, membership of Wirral Libraries gives free home access to the British Library 19th century newspaper collection.
To get free home access to the British Library collection of 18th century newspapers and a few 17th century ones (together called the 'Burney' collection) join Lancashire Libraries here
. Anyone resident in the UK can join.
Once you have got a membership number, access the newspapers via the Lancashire Libraries OnRL (Online Reference Library) page or take this shortcut - here