Yep, Brompton Bike Hire. Given their rental terms, I get the impression its more of a 'see how a Brompton fits into (and improves) your life for a day or several and maybe you'll like it and buy one' rather than an A-to-B transportation rental. Ideally this would be done at a store where a trained salesperson could talk to the rentee rather than at a vending kiosk, but Brompton has only one (pretty cool!) company store in all of the UK.

At his talk at the London Business School earlier this year Andrew Ritchie indicated he felt the bike hire effort was the wrong direction for Brompton, but if he elaborated on reasons they've escaped my memory.

Dahon partnered & prototyped a similar system several years ago, but I'm not aware it was ever implemented anywhere.