Thanks to all.   This is an Aussie car.   The break booster is mounted up inside the right fender well.  That is why I missed it.   There must be a check valve or something in there that is leaking by.   I have the car up on blocks so I might just be safe and install a new unit. 

I did plug the vaccum on the intake manifold and the brakes now work fine.  

Thanks to to all for the input.   

Booster problem... It would seem that as soon as you start the engine then manifold vacuum is activating the booster... and not releasing it until the vacuum leaks away.

Try bypassing the booster.

Cheers, Ian

You have the a too long push rod in the master cylinder. The autoX Mini in the picture had the same problem, slowly grinding to a halt, and had to be pushed (no pun intended) off the course.

you need to drive the car to see if you have a brake issue.  I had a mini with an booster

and the deflection of 1/8" in the pedal would put you through the windshield. Pedal

was right at the top. Not sure what happened when I had the engine off. It was years

ago.

Does it have a Servo fitted? check to make sure you have some freeplay twixt pedal and master cylinder.

This is really weird.  Something in many years of doing this I have never run across 

the car has been convereted to Cooper S dish brakes and drums in rear.  The master cylinder has been replaced and the brakes blead.  Everything feels good.  Emergency break cable has been properly routed.  The car is sitting up on a level set of ramps.  About 2 feet off the ground.   It rolls fine and the brakes feel good.  Everything appears to be normal.  Once you start the car the brake pedal gets hard and the wheels are locked up.   Turn the car off and wait about 15 minutes and the pressure will blend off and the car will roll again   

The car did this when I first picked it up   I have changed the Master cylinder and the problem actually got worse    This really has me stumped