Where can I find recordings of BBC Worldservice Radio, BBC Radio 4 and
BBC Radio 5 output from September 11 2001?

I'm looking for the actual on-air output as the story broke and
unfolded, not the end-of-day analysis. Similar to
http://www.bbc.co.uk/radio1/news/newsbeat/020829_911_audio.shtml,
except for BBC Radio 4, Radio 5 and BBC World Service, not BBC Radio
1.

Any format will do: Streaming Audio, MP3s, CDs for sale, Audio Cassettes

The British Library Sound Archive might have recordings of news
programs broadcast by the BBC on September 11th.  They do not record
everything broadcast, only specific programs of interest, however they
may have recorded news broadcasts later on that day given the extreme
nature of the event.

Their web site is here:
http://www.bl.uk/collections/sound-archive/nsa.html

You will be able to listen to the recordings for free, but you would
have to request permission from the copyright owner (in this case the
BBC) before making any copies.