I use InTune (http://www.smartcodehq.com/intune/). It sits in the menubar, and basically all radio stations exist. You just search your radio station in the box, favourite it, and then play or pause it whenever you want.
Soriko Radio is free (http://www.soriko.no/radio/), and to be honest, I'm actually preferring it to InTune which costs money. However, it sits in your dock and not the menubar. Still works great.
Thanks for recommending the app. The BBC stations are now added back in the UK playlist! Soriko Radio is soon getting its biggest update yet. I can't promise anything, but a menubar setting is on the list.
Looking forward to it myself! I submitted the iOS version this Sunday, next up is OS X.
Wakkaday: You can open your own URL using ⌘ + O. Finding those URLs depends on the provider. Most stations provide streaming links here in Norway on their website, but that doesn't seem to be the case in UK.
Regarding BBC - anything you're missing? I plan to add all BBC stations along with their local streams. Depends if they give permission.
Tunein Radio, simply a web page, no need for any specific app. Last one I looked 95 international, national & local channels BBC works perfectly in Safari etc.