Ah, so nearly there!
The "Curly Bottle/Ponytail Palm" is a good description of the one I saw with the exception that there was no red at all; it was all dark green just like BewilderedGreeny's photos:
"Beaucarnea guatamalensis, sometimes called the curly bottle palm... The leaves are similar in shape to those of B recurvata, but are a bit thinner, shinier and have more red at the base of each leaf where it sticks to the tree. And the leaves are 3Ã¢â‚¬â„¢-4Ã¢â‚¬â„¢ long and usually twisted. ...This species seems to branch from the base commonly..."
...BUT, oddly, the photos in the article, and elsewhere on that site, and everywhere else I've looked, are of straight-fronded plants which do not match the 'twisted' or 'curly' description at all!
When I enter "Curly Bottle/Ponytail Palm" into Google I get only that one site. No-one else mentions it, which is pretty surprising.
(Do NOT click the second copy site; it will download a virus
This is proving much harder than I expected!