You're right - it's down as a 1956 Elva-Climax Mk II.
(I say "down as" because , according to the excellent Specialist Sports Racing Cars by Anthony Pritchard (who sadly passed away a few days ago) the MkII wasn't introduced until 1957.)
Exactly!
It doesn't look like a typical Elva Climax Mk.II (or III) body, who made it?
It was For Sale recently and below is the blurb about it:
QUOTE
This 1956 Elva MkII race car is listed as a stalled restoration by the seller, who indicates this example is chassis number 100/60. It received a Coventry Climax engine and a new alloy body sometime during the ’80s, and is a late MkII produced just before the release of the MkIII.
UNQUOTE
You will note it's a 1980s rebody, which explains why it doesn't look like all other Mk IIs, but they say that it's a late Mk II, which doesn't quite fit the fact that it's a 1956 car and the Mk II only appeared in 1957...