Check the steering rack mounting bushings.....or possibly the rack itself....?

thanks for all the suggestions, I have a dedicated master for the front and one for the back, I have bleed the system more than once and all bubble free. I got the calipers with the bleeder on top. Thanks for the suggestion of the rear brakes Dlawson, I will verify. I was suggested to make sure the frame is not cracked, I'm heading to the look again. Thanks ErikG

Unfortunately, some Minis were made with horizontal braking.

I had unequal front braking once that was only corrected by a new  master cylinder . If it were a diagonal hydraulic system , I might understand that better, but I think mini is front/back. Whatever the problem was , it was not fixed until there was a new master cylinder, about the only thing you have not replaced

You have all sorts of new brake parts.  Take a look at the rear brake shoe position/orientation.  Reference the picture in the MM product link below for the RH rear brake assembly.

https://www.minimania.com/part/21A1058KIT/Classic-Mini-Rear-Brake-Backplate-Assembly-Right-Hand-W-shoes--Cylinders

Look at the friction material on the shoes.  Note how it does NOT extend all the way to the end of the metal arc.  If your RH friction material is not oriented as shown in the picture you may have a soft pedal and may have braking that is not balanced left to right.  The LH backplate and its shoe friction material orientation will be the mirror image of the picture in the link above.  While I doubt this is the only part of the problem, it could be a contributing factor.

Also, since you replaced so many brake parts, is there a chance there is still air in the system?  Did you get the calipers on the correct sides (bleed nipples at the top, not the bottom) ?

You said you fit new rubber flexible hoses in place of the old stainless ones.  Since rubber hoses are now installed, consider using clamps to squeeze off both the two rear brake hoses.  This will "pinch off" the flow of fluid to the rear wheel cylinders.  Take your car on a test drive with the rear lines clamped.  If the pulling to one side remains, it is a front brake problem.  Do NOT try this on the front wheels.  If you pinch off the front hoses and rely on only the rears the car will have very limited stopping power and will be unstable (may spin) upon braking.

It's possible the replacement caliper on the right is bad right out of the box, try checking how smoothly the piston moves in the bore and if it's harder to compress back in than the other side.

Tie rod bushes??? Although any decent aligner would have checked these out... Although, if they're not Mini savvy ???

Cheers, Ian

So I bought new front calipers, new brakes, new rubber hoses, new hard lines, flushed the system, bleed the system, had it aligned, and still pulls to the left. I also replaced the rear brake cylinders, adjusted and bleed the rear brakes. I'm frustrated What else can it be? what have I missed? Thanks Erik

Check the front tie rod rubbers/bushes...

Cheers, Ian

check your rear tire inflation also.  Low tire will steer the car from the rear under braking. 

Also you did one caliper. What's the chance that the other caliper piston is stuck or binding? 

check your rear tire inflation also.  Low tire will steer the car from the rear under braking.

Have you cleaned both discs thoroughly and changed the pads on both sides ?

If the caliper was leaking it has probably contaminated the pads, and you should never change just one side.

It could be the hoses but being braided that is less likely.  It could be your rear brakes are badly out of adjustment on one side.

I have a braking problem, when I brake my mini pulls hard to the left. So I changed the right caliper, it was leaking, flushed the complete system and bled the brakes. Went to test drive and it still pulls. I have steel braided hoses all around, could it be the hoses?