The usual three
Most UK agencies ask for a version of the same trio, and each piece has a different job. The covering letter introduces you and your book. The synopsis tells the whole story, ending included. And your manuscript's sample chapters prove the writing. Agencies differ in how much of each they ask for, so the exact package is always whatever their guidelines say.
Non-fiction works differently. Most agencies ask for a proposal instead. That means an overview of the book, a chapter outline, and a sample of the writing.
The sample chapters
The most common asks are the first three chapters, around fifty pages, or the first ten thousand words; each agency names its own measure. If your chapters run long, ending the sample at a natural break is fine. Whatever the measure, the pages come from the start of the book.
You cannot send chapter twelve because it's your favourite. Agents read the opening because that's what a reader in a bookshop meets, and because openings are where structural problems show. If your best writing starts at chapter twelve, that's worth knowing before you submit, and the fix happens in the manuscript, not in the package.
Formatting the manuscript
Agencies commonly ask for double spacing or 1.5 spacing, a readable font at twelve point or larger, and a Word document or PDF attached to the email, not a link to a cloud drive. Number the pages, and put the title and your name on the first one. If an agency states its own formatting rules, those win.
Formatting has never sold a book, but it does one quiet job: a clean, conventional manuscript lets the writing be the only thing an agent notices.
Partials and fulls
If an agent likes the package, they ask for more. Sometimes that's a larger chunk of the manuscript, perhaps the first hundred pages; more often it's the whole thing. Writers' forums call these a partial request and a full request, or just a partial and a full. You'll also see the package itself called a sub or a submission pack; same things, friendlier names.
A request for more is a genuine signal. It means the opening did its work and someone wants to keep reading. It isn't an offer, and fulls still come back with a no. But if you get one, something in your package is working.
Sending it
Read each agency's guidelines and build the package they describe, in the format they ask for. Some want everything as attachments, some want the letter in the body of the email, and a growing number use submission forms on their own websites.
Then keep a simple record of who has what and when you sent it. Response times run to months, and future you will be glad the record exists.