There is a range of "Internet radios" listed here:

http://corporate.reciva.com/products_and_technology/radio_products.asp
http://www.radioandtelly.co.uk/voyager.html
http://www.shop.bt.com/invt/cch256

I've never used any of them, so I don't know how restrictive they are (i.e. will they all let you play from your own stream or are the tied to whatever website they were designed to pick up their list of streams from), but it is somewhere to start.

One thing to be aware of is that the BBC on stream Radio 4 in Real and not all "Internet radios" can play Real streams.