I think it was a premium-rate number you had to call. When it became an app, it eventually had an ad-supported version with a paid, premium version "Shazam Encore" that was ad-free.
Yep, 50p a go from memory. Charged to your phone bill.
I used Shazam in London when it launched. I left the UK in 2003 so I reckon it was literally just as it launched. Presumably I saw billboards or a Wired article or something?