You have to add the kindle that you want to share it with to your account. I don't think you can share it with a kindle that has its own separate account
That link is to Amazon.com. I Can't find similar advice on Amazon.co.uk, and, following the instructions, the option to Loan does not appear on any of the content in my library.
Now that is a swizz, it does indeed appear to only be available in the States, if one were so minded one could remove the digital rights management from a book and lend it that way