BBC Radio 4 has been running a “neglected classics” segment on its programme “Open Book” where they get famous authors to choose books that not enough people still read. There are ten; there is a public vote; then the winner gets dramatised for Classic Serial.
The list is here, along with links to the authors talking about the books to help people choose.
Of those ten works promoted, only four are out of copyright (I was hoping for more than that, given that they are “classics”!)
So, four are available from Project Gutenberg, and can be downloaded for free as E-books:
Trollope, Miss Mackenzie (apparently very short by Trollope standards)
If you prefer your classics to be narrated, then two of them have been recorded for Librivox by volunteers, and can be downloaded for free as public domain audiobooks in MP3 format.