Ok, so here’s how it starts. The helmet looks basically like a ball, on top of a sleeve/collar.
I’ll start with a kid’s rubber-ish ball. I started by trying to stick the ball on a piece of cardboard tubing used for making concrete forms (it’s available at home improvement stores). But the cardboard cylinder does not “flare” out correctly. I tried to cut a ring of cardboard, then slit it and fold it in on itself. But it’s just not right.
Tube is for creating concrete forms 
Ball stuck into one end of the tube 
A cardboard ring 
The rough shape of a Mk V
The shape from the “globe” of the helmet, down to the base where it connects to the collar, is not a cylinder, it’s a conical section. I think a different approach is in order. If I pick point on the helmet where I think the sphere starts to flatten-out to the conic, and get a diameter there, then measure the base of the helmet, and those two diameters will form the top and bottom of my conic section.
This is really what the shape looks like. It’s a big arc. But I’m missing something on my math. 
I’m cutting 2 discs from cardboard/chipboard. 
The 2 discs for the conic section. 
I’m using some cardboard strips to create the sides of the conic section. 
Strips glued to the base with Weldwood Contact Cement 
AND…I see a problem. There shouldn’t be a “top”, since the ball has to be placed in there somehow. 
Top is gone, and I’ve added a few more strips. 
Here’s the test fit. 
Masking tape to hold it together. I think this is it.