.. no.
I kinda assumed I wouldn't be able to get one since I don't have any obvious sleeping issues. "I did my independent research and figured it would improve my sleep beyond the baseline" wouldn't work, I think.
What's the harm in trying?
(Lying to your doctor could be dangerous. So don't do that.)
Just say "I think my sleep could be better." It's true and baseline is vague enough that doctors don't mind improving people beyond it.
Doctors do get nervous when people they don't know come in asking for a particular drug, even something like melatonin or a hair-loss drug. This is much more likely to work if you have a regular doctor.
Going back to the original question, can you order it off of amazon.com (not co.uk)?
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.