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Getting ISBNs in the UK and Ireland
In the UK and Ireland, ISBNs come from one agency. Where you get them decides who is named as your publisher, which matters more than most authors expect.
Every country or region has a single designated ISBN agency. For the UK and Ireland, that agency is Nielsen. If you want ISBNs registered to you or your imprint, Nielsen is where they come from.
That sounds like a small administrative fact. It has consequences that are worth understanding before you publish, because the source of your ISBNs determines who the book trade believes published your book.
Buying from the agency
Nielsen sells ISBNs singly and in blocks of various sizes. Buying a block makes sense if you expect to publish more than one format or more than one title, since each format of each book needs its own number and they are used up faster than people expect. A single novel published as a paperback, an ebook and an audiobook already needs three.
When you buy ISBNs from the agency, you register as a publisher. You can use your own name or an imprint name. Whatever you choose becomes the publisher of record attached to every number in that block, and it is how your books will appear in the trade's bibliographic data.
Choose the imprint name with some care. It will sit on library records and retailer listings for as long as the book is in print, and changing publisher later generally means new ISBNs.
Free ISBNs from platforms
Some self-publishing and print-on-demand platforms offer a free ISBN. The trade-off is usually that the number is registered to the platform, not to you. The platform then appears as the publisher of record, or the book is listed under a generic label.
This can be perfectly workable for a book that will only ever be sold through that one platform. It becomes awkward if you later want to move the book elsewhere, because a number registered to one platform may not be usable through another. Moving often means a new ISBN, which splits the book's history across two identifiers.
Before accepting a free number, read the platform's terms about who holds it and whether it can be used outside their service.
Second-hand and resold numbers
ISBNs are not meant to be resold or transferred. Offers of cheap individual numbers from third parties should be treated with caution. A number bought that way remains registered to whoever originally obtained it, so the publisher of record will be someone else, and the book's data may be incorrect or disputed.
The only reliable way to hold ISBNs in your own name in the UK and Ireland is to obtain them from the national agency.
After you have the numbers
Obtaining an ISBN is only the first half of the job. The second is registering information about the book against it: title, author, format, publication date, price, extent, subject and a description. Bibliographic databases pass this data to retailers, wholesalers and libraries, and it is often the first thing a bookshop sees when deciding whether to order.
Nielsen runs a bibliographic database that publishers can submit title information to, and much of the UK trade draws on it. Registering the details there, accurately and early, is what turns a number into a book that can be found.
Keep your own record as you go. Note each ISBN, the product it was assigned to and the date. A spreadsheet is enough. The point is that no number is ever used twice and that you always know which one belongs to which format.
Getting ISBNs is not difficult. Getting them from the right place, in the right name, saves a good deal of untangling later.