It's always a good idea to bench bleed the master cylinder. Just make up some lines that go from the master cylinder outputs and loop back into the reservoir. Stubs with clear plastic tubing works well. This will confirm that the master cylinder is working.

Kelley

I just went through this with my Mini with the exception of replacing the master cylinder.  I just followed the advice of everyone who responded to my questions and got through it.  One of the things that I found was that my handbrake wasn't set right as it was too tight essentially applying the rear brakes on its own.  You always want to bleed the rear brakes with the handbrake fully released.  I also did what Mini 14 recommended to remove the brake pads, insert someting thinner than the new pads and allow the pistons to extend then press them back in.  Additionally, while I was pressing the pistons back in I also opened the bleeder to get any trapped air out from the calipers.  When I first started to bleed the system I couldn't even get the pistons to take up the slack between the them and the pads.  After doing this, my brake pedal travel was was greatly improved and is now firm without any sponginess.  

Maybe convince yourself that the MC has an issue by bleeding it right there before changing it.

 Thank you all for excellent advise.I'm going to start by changing out the MC.The one I installed was new but,even new can be defective.

  All suggestions are great and I really do appreciate everyone's input and help.

    Cheers,Dave

+1 for Mur's advice.  Crack the joints open working from the MC out to the furthest point.  When you see fluid come out of each joint you know the fluid has reached that point and hopefully pushed all the air ahead of it or out.

However, the B is likely to have some of the same issues that the Mini would have so the same caveats would apply. 
1) If you had the calipers off, make sure they are correctly re-installed, bleed nipples "up".
2) If you had the rear shoes off, make sure they are on in the right position.  The shoe will have the friction material "relieved" at one end of the arc.  On the front shoe, that relieved area goes at the top.  On the rear shoe, the relieved area goes towards the bottom.  Put them on in the wrong place and the pedal will remain "squishy" or just not feel right.
3) Lastly, properly adjusted rear brakes will not allow an elevated wheel to "free-wheel".  When properly adjusted an elevated wheel will spin through a little more than one rotation and you should be able to hear and feel drag.  Looser than that will result in excess pedal travel.

I can only tell you what I would do in the same situation. Jack up the whole car if you can and remove all the wheels. Adjust the rear brakes to full on, as tight as you can get them with the handbrake off. I mean tight. You should not be able to rotate the drums at all and then tighten them some more. Blead the rear brakes starting with the one furthest from the master. You may get a little pedal at this point. Move on to the front. Start with the caliper furthest from the master. Remove one brake pad. Replace the removed pad with a VERY worn pad if you have one. If you do not, use a screw driver and place it between the rotor and piston. You want to make sure that the piston can not come all the way out of the caliper and expose the seals. Push the brake pedal so that the piston moves toward the rotor but does not come all the way out. You will need to pump slowly a couple of times. Then compress the piston and put your new pad back in. Do this for all four pads. Then blead the brakes as normal starting with the one furthest from the master. Have fun and good luck.                 

I think your master cylinder rebuild was not a success.  I always begin bleeding right at the MC, where the lines are loosened, a rag is placed where the fluid will seep, the pedal is depressed slightly and then the lines are tightened before the pedal is allowed to come back up.  Once you get clear fluid there, move along the lines to the various shuttle valves and connectors and calipers and wheel cylinders.

Use the appropriate Haynes manual for your particular car for guidance.

Make certain that you have a helper that understands not just the process, but why certain steps are done.  Stabbing violently at the brake pedal, manic pumping or letting up at the wrong time will often wreck the chance of getting a good pedal.  Don't move quickly, don't run out of fluid and always run a line from the bleeder to a jar so that the end of the line is immersed in fluid and a pedal that is released when a bleeder is still open isn't the end of the world.

 This pertains to my '72 MGB GT.I figure most Brit brake systems are the same.

 I recently overhauled my brake system.New calipers,rotors,drums,wheel cylinders,& new master cylinder.The problem is this,I can not for the life of me get these brakes bled.I have no visible leaks.I tried using silicone fluid and thought that might be the problem.Completely flushed the system and used Valvoline 3/4.Still no brake peddle.What am I missing?I've never had brakes that wouldn't bleed.Any ideas?