Then I happened upon the Selsey Birding Blog and a report of two Black-Winged Stilts at Medmerry. As far as I know the news wasn't put on RBA/Birdguides/Sussex Birding so I put it out. Thankfully, a few more people got to see them than otherwise might have been the case...
A bit of a shaky video here of the Stilts:
https://www.youtube.com/watch?v=F8YiK6eVCBI&feature=youtu.be