Yes, Ian, my Series One is like that too. I haven't touched the Lancia's headlining, but many years ago I replaced a similar one on an early Triumph Herald: the front and rear screens had to be removed as the cloth lining is trapped by the rubber seals. when the front and back sections have been released (oh, and the sides which are held by the door seals), the wire tensioners just unclip and the entire lining falls into your lap.
Replacement was as so often described in Haynes manuals - a reversal of the previous procedure! Clip the tensioners into position, and then stretch front back and sides and replace all seals ... Good luck!