I tried to locate a copy of 'The Shiny Men Again!' in 1982 (record issued in 1981 ?), to no avail.
Info from the Whatt's Rattlin' newsletter (http://www.musart.co.uk/watrat/wr14.htm
"About Canterbury-like bands and albums, a group called The Shiny Men has made an LP called "Again!" LP, featuring RW on one song. It came out in 1980 (or 81), and it is quite rare (and expensive :-|) because it is on a quite obscure sub-label of United Dairies, the highly-collectable label of Steve Stappleton and Nurse With Wound. The music sounds a bit like a Rock- In-Opposition group, Henry Cow and that stuff, maybe also Hatfield and National Health, but then transplanted in the beginning of the 80s."
And also (with cover art) from http://perso.club-internet.fr/calyx/cantdisco/S.html
The SHINY MEN - Again!, 1981 (Experimental)
Chris Lavelle (voc/g/comp/lyr) - Chris O'Neill (kb) - Jerry Soffe (b) - Frank Hockney (d/pc)
with: Robert Wyatt (voc ) - John O'Neill (s) - Jim Stuttard (cl) - Andy Robinson (tub) - Laurie Linton (bv)
Rec: 1981 - Loc: Berwick Street Studios, London - Pr: The Bombay Ducks
Tracks: 1. One Of The Big Shiny Men - 2. To A Spaceman - 3. Dream Pussy - 4. Secret Monkeys - 5. Ape Ship - 6. C Jam Bop Larrence Funka-Monk-a-Blues - 7. Cheap Emotion - 8. Too Wonderful - 9. Back Back - 10. Institution - 11. Model Citizen