Firefox. I've tried everything, FB Purity doesn't work, allowing it then disallowing it in the browser didn't work as was suggested. The only way I believe it can be prevented is if someone was to write some kind of script / browser add on that prevents the message, blocks it somehow.
As a result of this I'm no longer updating my fb account I will hardly be using it. I'm certainly not clicking 'Turn on' again. I think fb are are trying to gain access to my desktop. Why else would there be no 'Don't ask again' option. Or a setting that allows you to disable notifications permanently or allow them if and when I choose to.