Okay, I've managed to track these down.
The following URL's take you to high quality 320K streams of the appropriate stations and can be pasted into VLC Media Player or similar.
Note that these streams will not work unless you're a resident of the U.K. BBC Radio 1 http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_one.m3u8 BBC Radio 1Xtra http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_1xtra.m3u8 BBC Radio 2 http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_two.m3u8 BBC Radio 3 http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_three.m3u8 BBC Radio 4 http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_fourfm.m3u8 BBC Radio 4LW http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_fourlw.m3u8 BBC Radio 4 Extra http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_four_extra.m3u8 BBC Radio 5 Live http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_five_live.m3u8 BBC Radio 5 Live Sports Extra http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_radio_five_live_sports_extra.m3u8 BBC Radio 6 Music http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_6music.m3u8 BBC Asian Network http://a.files.bbci.co.uk/media/live/manifesto/audio/simulcast/hls/uk/sbr_high/ak/bbc_asian_network.m3u8
