There is a detailed website which links to a video about it (which, unfortunately, has a strange echo when Woolf explains the idea). The site claims that it has been "patented worldwide" but I couldn't find any granted patents -- I think they mean that they have applied for patents worldwide which is a different matter.
World patent application Collapsible helmet has the main drawing shown below.
There are a number of panels joined to each other so that it folds down the middle to form a slim shape. The World search report at the end of that document cites an American patent as having some similarity, Roy Shifrin's Foldable padded helmet. Its main drawing is shown below.
Incidentally, while many British cyclists use protective helmets, they are little used on the European continent.