Hi there, Bertie!
Thanks for posting in the Apple Support Communities. I understand that you're trying to purchase music from the iTunes Store on your iPhone, but every time you try you get prompted to sign up for Apple Music. I'm happy to help!
It sounds like you're browsing music in the Music app. While this is where you would listen to music you've purchased from the iTunes Store (as well as songs you sync from your computer and Apple Music if you subscribe), it is not where you make the actual purchases. That is done in the iTunes Store app. In iOS 13, this app is a white start on a purple background.
Cheers!