OK, that picture of "Clay Nicholls and the Blue Flames"...
Concentrating on the white or blond guitar held by a player captioned as Tony Harvey, it is possible that this is the mystery guitar. Only "possible", mind, certainly not definite (though I ask myself how frequently players were able to change guitars in that era and am also open to the possibility that the guitar was borrowed.
https://anonimag.es/image/JT9sDGoEven more so than Paul Day, I am not familiar with every guitar on the market in the late 1950s, but that guitar, though it might (and equally, might not) be referred to on the associated web-page as an Egmond, does not look like an Egmond to me. Egmond guitars were renowned as being cheaply made, cheaply appointed, relatively unpleasant to play and generally of lower quality. It is no exaggeration to say that contemporary Japanese production - especially by the company turning out Antoria / Guyatone models - was of better quality than Egmond were able to do at that time.
Turning to the guitar in the picture, that does not look like any Egmond I have ever seen (with the proviso that I cannot claim to have seen them all). It looks very
German, with its typically-Bubenreuth-styled fretboard markers (think Hofer Verithin) and the three pickups, a feature common on (say) Framus. The tailpiece is definitely German. The pearloid (or similar) inlay on the headstock is a feature seldom seen on any guitar not made in Germany. I think that inlay looks hideous, more suited to an accordion, but that's another point. Headstocks of that sort look best in black with the maker's name inscribed in pearloid - as near to the tasteful standard set by Gibson in the 1900s as possible.
The same model of tailpiece was used on the Hofner President and associated models as well as on other German brands and even on the Harmony H75 / H77 (made in Chicago). It wasn't made by Hofner and would have been available to other makers as OEM (in fact, it was), but it will have been - in wholesale terms - an expensive component to buy in. And Egmond were perfectly capable of producing tailpieces. Of all the criticisms of the Lucky 7 that I have heard over the years, not one of them has ever been about its tailpiece, which was perfectly serviceable.
So... bearing in mind that at the time, the Gretsch White Falcon was a single-cutaway guitar, this guitar - whatever it is - has to be in the frame, though the Grimshaw SS (which has the added bonus of looking more like the d/c White Falcon and of probably being available more readily as a loan because it was in Bruce's keeping for a while) is still, I suggest, also in the frame.
PS: If you want some real b******s to read about guitars, try this Wikipedia entry:
https://en.wikipedia.org/wiki/Antoria