It was 'Teef's recommendation!
I'm now at Langland Bay House, which looks ok but isn't quite so conveniently located (ie I have to ride up a bonus hill to get there when we've finished our long, leisurely brunch)
I tried half a dozen places: it looks like the town is pretty full that weekend. If anyone isn't booked yet, don't delay, or you'll end up in Llanelli!
That's very close to Chateau Claud. Susie will testify that the route there from the pier is as close to pancake-flat as makes no odds. Well, alright, there's a surprise slope on it that nearly had Dellzeqq's front wheel in the air, and the rest is a relentless drag on beer-heavy legs. But you get to go past Catherine Zeta-Jones's house! You're right on a fab beach there, Frank.