The ISBN (International Standard Book Number) for the self-publisher is important, so gets a special mention. The ISBN is a unique reference, normally printed on the back cover of a book. It is used by publishers, booksellers, and libraries for ordering, listing, and stock control purposes, and has an impact on book distribution. However, there is no legal requirement to allocate an ISBN to a book. In the UK, Nielsen Book run the ISBN Agency for the UK and Ireland, but there are other agencies worldwide. Although it can be a hassle to set up, I recommend that self-published UK authors assign their own UK ISBN.
The self-publishing providers' use of the ISBN is not always helpful to the unassuming author. For instance, Amazon's Kindle Direct Publishing (KDP) can provide a free ISBN during paperback setup, BUT because Amazon is a US company, KDP will assign a US ISBN (supplied by Bowker, the US ISBN agency). A US ISBN is fine if an author wishes to sell their book online, and make use of Amazon's external distribution features that apply in the US; however, if the author wishes to sell their book online, and make their book available to UK book retailers and libraries, then a UK ISBN must be provided. However, UK ISBN numbers are not free.
How does a UK ISBN work? Every book that is assigned a UK ISBN number is held on Nielsen's database. So, when a customer requests a book through a UK bookseller or library, which is not held in stock, a search of the ISBN in the database will bring up the book's bibliographic data, such as the publisher and distributor. The book can then be ordered directly. With traditional publishing, the publisher will generally be a large organisation who has a distributor tied in. With self-publishers, the individual author is the publisher and distributor; therefore, responsible for providing the book to whichever bookseller has ordered it.
The pros and cons of a UK ISBN. For the self-publisher, the idea of having their book requested by a UK bookseller is attractive, but it can be a financial disadvantage. Self-publishing providers generally offer a print-on-demand (POD) service: each time a customer buys a book online, a request is made to print the book. There is no wholesale stock as such. Booksellers want to make a profit (they won't order a book at the retail price), and so they tend to ask for non-negotiable discounts that are not favourable to the self-publisher. This can result in maing only pennies in profit for the author, more likely a loss, even when they can buy their own books at a discount. However, one advantage of a personal UK ISBN is that the author has total publishing rights over their book, and can control what they do with it. With many US-based self-publishing providers, if an author accepts a free US ISBN, the publishing rights belong to that provider. (This is not the same as copyright. The author retains copyright of their work wherever it is published.) This makes it difficult for the author to make certain decisions, such as removing a publication, if they don't have control over their book. And once an ISBN has been assigned, it cannot be changed.
How to obtain a UK ISBN. The quickest way to buy an ISBN is to order directly from the ISBN store. Registration is required, along with a reasonable amount of form-filling! As at January 2020, a single ISBN costs £89.00. 10 cost £164.00. A unique ISBN is required for each type of published media: paperback and e-book (so that's two for a start!) However, in order to register to buy an ISBN, the author has to provide a publishing name (imprint). This is worth consideration, and it can be a trading name or a personal name.