Drupal 7 audio players not working correctly in Chrome and IE

I'm using the Audiofield module to add mp3 files to a site, however I'm having trouble with all the players I've tried (eg Wordpress Player, jPlayer, Flowplayer etc).

In firefox, the mp3 files play just fine, the controls of the players all work (eg the track buffers, and can be skipped to a specific part of song), and the pause button works etc.

In Chrome, IE, and Android browsers (and possibly others) however, the player doesn't work correctly. Although it will start playing the song, it doesn't buffer the track, and says "Connecting" constantly, and then anytime you click on the timeline it just starts the song over from the beginning. Also the time doesn't display correctly.

I'm using a Private file system if that matters.

Does anybody know how to get this working properly in anything other than Firefox?