I use builders' band for all sorts fo DIY tasks - last one was a strap to hold the car's radiator header tank up off the engine wiring! To be honest, I can't see it being strong enough for Windsor chair back bending.
I went to the open day Axminster held for us all in the spring of last year, and watched the steam bending demo too (I think they ran it several times that afternoon): the machine Paul Styles uses exerts a huge force. I remember him saying it was originally bandsaw blade (I assume an offcut from before the teeth were cut), and I think he was pulling the ends with a boat trailer winch. Bandsaw steel would be ideal if you can get it, bur Paul's got somewhat privileged access!
You might try several strips of builders' band together - I fold it back on itself for extra strength sometimes, but if you look at a single strip, although it's about 3/4" wide, the holes in it make it quite a lot weaker in tension than you might expect. It's also probably really cheap Chinese steel, with who-knows-what scrap chucked into the furnace.
I think I'd test it somehow, in case I found it wasn't up to the job when I had a piping hot piece of oak in the jig.
E.