First you need to disable Chrome's built-in PDF viewer:

• If you're using Chrome v 57 or later, type chrome://settings/content/pdfDocuments into the address bar, and make sure the setting is set to download or open PDF files in a different application, instead of automatically opening them in Chrome.
• If you're using Chrome v 56 or earlier, type chrome://plugins into the address bar, then scroll down and click Disable next to Chrome PDF viewer

Click on the link in the email from the British Library.

On the next page, click the link to download your document.

The Save As dialog box opens.  Choose a folder to save your document in, and click Save (see the screenshot below).

Follow the instructions in the Logging In To Your Document tab.