The answer

Scan of a frond of Athyrium filix-femina 'Caput Medusae'

Thanks for all the responses to my challenge to identify the mystery plant. It is indeed a form of the Lady Fern, Athyrium filix-femina, and as Michael guessed, it is the clone called 'Caput Medusae'. Marie clearly came very close too - and I am intrigued to know how the Danish 'curly kale' fern looks.

'Caput Medusae' is one of the most extreme variants of its very variable species, with the frond converted into a dense tuft of intertwining growth at the top, forming a series of tight and rather hard balls of proliferating tissue. There is no sign of sporangia. The whole plant is no more than about 20 cm high and the resemblance to parsley is remarkable. I tried to ge an image of it tonight using my scanner, but the result (above) was more curious than informative.

The only information I can find about its origin is the note 'raised by Mapplebeck' in Charles Druery's British Ferns and their Varieties (1910). John Mapplebeck was one of the great Victorian fern enthusiasts, whose name is attached to a good crested form of Dryopteris affinis, 'Polydactyla Mapplebeck'. I was given it by a kind friend in Ireland, but it seems to be rather a rare plant, and very desirable to judge by the reactions of visitors who see it - there is a waiting list...