Liverpool Libraries now have over 3000 free books to download.You have to be a member of Liverpool Libraries and can apply to join in person or online.
I opted for Liverpool Central Library as my main library and was not pleased when my ticket arrived which has to be activated in person within 30days, but the enclosed letter stated that as a non-resident of Liverpool I could not have e books, a fact not mentioned on their website.Even residents of Crosby are e book barred as they come under Sefton Council.Apparently it is to do with Internet agreements.
I am glad I did not buy a Kindle Fire or similar for this purpose.Basic Kindles cannot get the Liverpool Library downloads.
Now I have to trek over and carry the books which I suppose is better than nothing.
Wirral libraries have e books but not many.
If anyone is thinking of buying the Kindle HDX I found it was £30 cheaper at Tesco Online than in their store.

Have you tried logging in to this site using your library card and pin number?

Liverpool library - http://liverpool.lib.overdrive.com/