Unfortunately, I don't know anyone with a Spitfire so I can't compare but from your picture, it seems the one in the picture should work. It might be that maybe the right turn signal is set but I think it's probably because of the angle of the picture.
I would be very surprised if Chunky used a minor variation of a BMC Lucas part. I think it's much more likely that he chose standard off the shelf parts. IIRC, the turn signal at Victoria British was somewhere in the $35 range. If they'd be willing to take it back if it's the wrong one, I'd get one and try it.
One more thing. The Golden Gate Lotus Club did a parts cross reference (
http://www.gglotus.org/ggpart/europacr.htm) and gave the Lucas part number for the dimmer/turn signal/horn stalk as:
TC, SP Turn Indicator / Dimmer Switch Lucas 163SA 30370
You could use that number to ensure you're getting the right one.
Edit - last minute thought:
One last thing. I happen to have a spare dimmer/turn/horn stalk and I can see how I fixed the one in my car. The clamp on mine broke. I sawed a slot "behind" where it broke and anchored the strap there by bending it to hook in the slot and wrap around like the rest of the clamp. Does that make sense? If only your clamp is broken and the plastic is in decent shape, you might be able to get away with doing something similar.