This sounds very much like you have a leak on your braking system servo vacuum circuit.
The vacuum to operate the servo is generated directly from the intake manifold AFTER the carb throttle valve. So a lean on this circuit has the same effect as opening the throttle. Also the brake pedal will go hard due to the loss of the servo assist generated by vacuum.
You need to carfully check the hose going from the brake servo unit to the inlet manifold for damage, splits, etc. This may be a non metal cloth braided hose so spotting damage may be difficult.
You also need to check the servo is holding its vacuum and the diaphragm is no broken. This can be done as follows (assuming you can get some vacuum generated by the engine).
1) Run engine and listen for any continual hiss/air leak sound
2) Engine running check brake pedal feels normal
3) Switch off engine and wait say 15 seconds
4) Press brake pedal. Pedal should feel normal and you will hear a faint hiss
5) Release brake pedal and repeat 4)
6) Repeat 4) & 5) and on each repeat the pedal will get firmer as the vacuum is lost
After servo and hose checks if the problem still persists then the intake manifold and gaskets will require investigation.
