Well, today was a success.
I took all of the advice here and set about broaching a 3/8 hole in 1" of steel. Before the broaching was carried out, I had to make a new shaft that was a close fit to the guide and spend some time ensuring the shaft was perpendicular with the press table. I then started the broaching, releasing pressure, as suggested here and also to adjust the table in increments as the broach is about 12" long!
The previous attempt at broaching was with an unbranded tool from our Eastern friends, it bowed significantly and did not cut straight, eventually snapping, this broach was a US made Dupont, an excellent tool, it did not bow at all.
I was a bit apprehensive and went very slow feeling for feedback of binding and was a bit careful as each tooth popped out of the bottom of the work. But as the broach got shorter, it went quicker and with plenty of pressure releases to check for bowing etc, the cut was complete. The square is perfectly concentric and did not wander of course one bit, as you can see by the witness marks left by the guide hole, each side was exactly the same.
Thanks to all here who offered their valuable time to respond, I recommend buying tools that are not from the cheapest source, the Dupont broach, as far as broaches go, is of supreme quality and if it is treated with respect, this broach will cut 1" thick steel without tears!
I have posted a couple of pictures, those with a keen eye will note the work is a pair of crankshaft cheeks for a Hodgson 9 cylinder radial. I will post work in progress soon, but after Terry's excellent thread, I think you are all a bit bored with radials.
Steve