I have had this problem as well. I had my friend sign up and when it wasn't working, I had her try signing up using her FB instead with both a link and an email referral and neither have sparked an email with the code in it. Not sure why. Have thoroughly checked both my inbox and my spam box and haven't received anything. Contacted Spotify support by e-mail and have yet to receive a response there either (Not to mention how lousy they've been in the past toward me. No offense. I used to work customer support and good Spotify CS is so incredibly rare its disgusting.) I, like this other person, would like to know why I haven't gotten a referral code e-mailed to me and if it could possibly be fixed, WITHOUT having to jump through a thousand hoops to get a proper answer.
I do sympathise but the only support they offer for the referral programme is via email. You could try getting in touch with the support team via the standard contact form to see if they can help. If you get an automated response directing you back to the community or to the help pages, make sure to reply to it directly to speed things along.
Thank you so much. It really means a lot. According to one of my friends, the same thing is happening with her and I keep seeing it on the forums so I'm guessing it's a common problem with the system not sending out the codes, but at the same time it's super frustrating!