Allan, are you sure? That last picture looks like B3, Lesley Marr's streamliner that was rebodied into the 'toothpaste tube'
There was only one C-Type. It was completed by Paul Emery after Connaught had gone bust. It ran in one GP, the 1959 US GP from which it retired on tjhe first lap. It was then supercharged and failed to qualify for Indianapolis. I don't have a picture to hand, but I'm certain it didn't have a 'toothpaste tube' body. As the C-Type had a de Dion rear end and inboard rear brakes, the original photo has to be a B-Type Syracuse
All the B-types had Alta engines originally, as opposed to the Lea-Francis engine in the A-type. Hence the unofficial Connaught-Alta name is sometimes used.