Aha but if I use the .pls URL, the steps work perfectly.

URL is "http://open.live.bbc.co.uk/mediaselector/5/select/version/2.0/mediaset/http-icy-aac-lc-a/format/pls/vpid/bbc_radio_three.pls"

Audio Info shows:

Input Processing
Source: "http://bbcmedia.ic.llnwd.net/stream/bbcmedia_lc1_radio3_q?s=1446205564&e=1446219964&h= b85bdda2e7b0de9e50fddf148901675b"
Decoded to: Stereo, 16 bit, 48 kHz
Rate: 321 kbps

I can switch stations and BBC R3 comes back

It shows as No Title in the Playlist, presumably because this is what it's defined as in the .pls file:

root@moode:~# cat bbc_radio_three.pls
[playlist]
NumberOfEntries=2
File1="http://bbcmedia.ic.llnwd.net/stream/bbcmedia_lc1_radio3_p?s=1446205564&e=1446219964&h= d4d8d410385e6bc5b68601dbb947cecf"
Title1=No Title
Length1=-1
File2="http://bbcmedia.ic.llnwd.net/stream/bbcmedia_lc1_radio3_q?s=1446205564&e=1446219964&h= b85bdda2e7b0de9e50fddf148901675b"
Title2=No Title
Length2=-1


Rob