Audible offers various membership plans, with £7.99 per month allowing you to purchase one audio book per month, £14.99 per month allowing you to purchase two audio books per month and annual plans based upon the foregoing two. Members also get unlimited access to audio content to the 'Plus Catalogue'. You can pause or cancel your membership at any time.
There's a free 30-day trial available, which allows you to download two audio books:
https://www.audible.co.uk/
Audiobooks.com is a rival service, with £7.99 per month getting you access to one 'premium' book and one 'VIP' book. (See the website for an explanation). There's a 30-day free trial, including access to two audio books. (Actually, it might be three free books; the website says 'two' on the home page but 'three' on the sign-up page):
https://www.audiobooks.co.uk/
Kobo.com works in a similar way, at £6.99 per month for 1 title, with a 30-day free trial:
https://www.kobo.com/gb/en/audiobooks
With regard to access to audio books from county library services, it's worth remembering that some library services offer membership to people who live in neighbouring counties (or even further afield). For example, you can join Suffolk Libraries via an online application if you live in Suffolk, Norfolk, Cambridgeshire or Essex. (You can also join if you can show that you study or work in the county, or that you're visiting an address in Suffolk, but only by applying in person, rather than online).
So, if you've exhausted everything that your own county library service has to offer, it might be worth finding out if neighbouring services are also accessible to you.
BBC Sounds gives you free access to (usually abridged) audio versions of books which have been broadcast on Radio 4:
https://www.bbc.co.uk/sounds/category/audiobooks