Lee,
I don't have any concerns from the images I've seen that the Sussex and Kent birds are Oriental (the same bird i assume!).
The basic jizz, with the short-back end kind of shouts Oriental and is quite marked from Collared Pratincole. Further clues are the rather subdued upperpart contrast, mid-way between Collared and Black-winged, but closer to the latter, and rather "chunky, thick-necked/bodies look, which give a shape that's rather compact, moreso than typical Collared.
I haven't seen them in a while so i can't comment on features such as thickness of tailbands, but the long-legs projecting past the tail is a pretty good sign to run and call Bird Alert!
The tips to the secondaries has often come up in pratinocle id..but in Collared, the bases to the secondaries are rather dark, especially on the outers, so you get a dark border along the upper edge of the white tips. I'm unsue as to how to age first-summer pratincoles without research but the Pagham birds feathers don't look too worn and appear the same length and I find it more surprising that if the tips to these can wear off, that they would do so with such uniformity along the length of the wing...and, if they were worn feathers, i would expect the exposed tips of all the secondaries to be really knackered and frayed, more so than shown in the images.
Pictures of the Kent bird seem to show quite a bit of red on the mandibles, probably a little more than I've seen on other images of Oriental, but probably well within the range.
I remember seeing pix of bird in Kuwait with some note about nostril shape, but I'm not too sure i'd put much use into that!
I was lucky enough to see the Gimmingham bird the day it was found ( a real mega back then!) and watched it on other occasions performing superbly..pratincoles are one of my favourite families..I wish I had a camera back then!
Julian Hough