I can't remember who I was talking to yesterday, but somebody was suggesting the stilt was a male due to the dark crown, nape and hindneck; I thought a dark crown, nape and hindneck suggested a female, turns out we were both wrong (as is the Collins Guide).
Turning to Himantopus himantopus himantopus in a few venerable tomes (as you do), BWP describes breeding adult males as "Crown down to eye, nape, and hindneck black, frequently intermixed with all or partly white feathers, rest of head and neck white; occasionally, all head and neck white, except for some black-tipped feathers on hindcrown or nape; exceptionally all head white" and breeding adult females as "Head and neck white, frequently dappled black on nape, crown, or upper hindneck; at times, even darker than male partner."
Well that's all as clear as mud then. 'Shorebirds' is a touch less nebulous stating "sexing by head pattern is hazardous owing to individual and geographical variation; in most populations is likely to be whiter-headed than female" I think may well be where I got my 'white head = male' from, they then go on to describe adult male as "Crown and hindneck patterns vary from pure white to dusky-grey, but black patterning of other races is absent" and adult female as "crown and hindneck patterns show same extent of variation as in male."
Praters 'Holarctic guide' is the only one to really cut through the bollocks though with "All colour patterns of crown and nape occur in both sexes". Well that's sorted that out then.
PS. I did remember the Elmley birds correctly, the male of the pair was the white-headed bird (see here).