welcome to the forums.
BBC Radio 1, 2, 3, 4, 4 (LW), 4 Extra, 5Live, 5Live Xtra and 6 Music play A/OK on my SoundBridges.
Are you trying to play the BBC stations from your SoundBridge's Presets or from your Favourites?
SoundBridge M1001 and M1000 • Clint L1 (retired) • DNT IP-dio (retired)
Google Chromecast • Amazon Fire TV • Amazon Echo and Echo Dot