This is actually a limitation of the web interfaces for Rdio, MOG, Grooveshark, and I'm assuming google and amazon's cloud player as well.
EDIT: Just found this http://getfactotum.com. But it'd still be better if there was some HTML5 support for it since the app only works on specific sites.
Yes, I've implemented this kind of thing with http://player.fm and it's really a fundamental limitation of the HTML5 audio tag.
iOS is actually very cool in this department as it treats HTML5 audio as a native audio track, so it works with bluetooth controls, the play icon shows up in toolbar, works in the background, etc. Everything native audio does.
The reason next/prev doesn't work is because HTML5 audio has no concept of a playlist. It's just a dumb audio tag with exactly one source URL to play. So iOS really has no way to map what's going on in the browser into the usual concept of a playlist and it has no API to call to move to the next or previous track.
It's still well ahead of the other mobile OSs though, in the way it does at least treat HTML5 audio as standard audio, to the extent that's possible.
