There are many sources of audiobooks on free loan or economic purchase, including:
A wide selection of audiobooks can be downloaded free for 2 weeks (can be checked out again if still available).
Lots more cassettes, CDs and MP3 CDs are also available to rent for 60p.
About 800 audiobooks (mainly ChickLit) are available free for 3 weeks (extendable).
Fortunately most are in mp3 format now, probably because of all the problems with digital rights protected files.
Many more cassettes and CDs are also available to rent for £1.
Choose eAudiobooks, decide if you want to Show only available titles, choose which grouping or Category you want, or pick a Featured book to Preview and/or Borrow. Each book has a short summary and audio preview (which does not work on all platforms).
A vast selection for £7.99 a month. Membership covers one book a month (after one month free trial) and reduced price offers for additional selections.
Recommendations from their UK Book Club.
LibriVox free public domain audiobooks are read by volunteers from all over the world.
1000 free audio books and much more.
Read by human volunteers or computers.
Previews
You can listen to short audio previews from a number of sites, including Library, Audible and GoodReads.
Some publishers put previews on YouTube, such as Macmillan and you can even listen to all George Orwell's 1984 in 14 parts.
Try searching in Google "free audio books" to find other sources, including booksshouldbefree.com