One of the pieces is a diary of a trip he made in 1960 to the U.S. for a couple of conferences and to meet various people. The introduction, written by Beer for the 1994 publication of the book, ends with what it describes as a technological postscript:
'The Diary was recorded each night on a hand-held battery-driven fine wire recorder. It was a much admired innovation, for this was before portable magnetic tape recorders were available. In the early 1950s, I had been Production Controller of Samuel Fox & Co., which was the special steels branch of United Steel. We supplied the fine wire which I think was 0.001 inch diameter. At any rate, if the wire broke the spool became shrouded in what looked like a mist, as the wire unspooled, it was so fine. In 1960 we still expected a huge commercial success with this product - eclipsed in the event by magnetic tape.'
I commend to you this page on the Minifon Wire Recorder, marketed in the UK by EMI http://www.pimall.com/nais/pivintage/minipon.html It is an attractive device, and I like to think that Beer had one of these. Note in particular the watch microphone and the body harness, back when 'wired for sound' really meant something. They were obviously more widespread than I realised.
As ever, so many obvious Google searches reveal no hits or nothing of interest.
They are surprisingly cheap on ebay, although of course it is not clear that any of them work, and I don't want one anyway.
(interesting factoid - the first commercial Black Box Recorder was based on one of these http://en.wikipedia.org/wiki/Flight_data_recorder (WSMNBTO))