If you’ve rebuilt your brakes, then bled them and the pedal travels a long way before anything happens, what’s happening? Pumping it once has an effect, but not permanently. If you bled them repeatedly, what else can you try?
Well… firstly, check that the rear drum brakes are correctly adjusted. Jack up each wheel in turn, then rotate the square-headed adjuster at the bottom of the backplate until the wheel stops. Back it off until the wheel just rotates without resistance. Also make sure that the handbrake is properly adjusted. It should firmly apply to both wheels after four or five clicks.
It’s possible that there’s still air in the hydraulic system. Bleeding can cause the fluid to fill with tiny bubbles. Rather than bleeding it again, allow the car to stand for a few days. The air will tend to find its way to the top of the system (usually the master cylinder). Operating the pedal slowly a few times will encourage it to escape from the cylinder and into the reservoir.
Sometimes, the air collects in the loop of steel pipe that comes out of the top of the master cylinder. In this case, prop the pedal partly down overnight and rapidly remove the prop in the morning. This will tend to suck the air into the master cylinder. Check the master cylinder seals by pumping the pedal twice, then pressing it as firmly as possible for 30 seconds. It should stay in position and not sink towards the floor.
Occasionally, bad design leads to air pockets trapped in parts of the system, such as vertically-mounted brake light switches or front drum brakes with the only bleed nipple on the lower of the two cylinders. In these cases, slackening the nearest union and bleeding it into a rag will chase out the air.
If all this fails, remove the rear drums and shoes and place them inside one another. Standard size shoes running in an oversize drum will tend to cause excess free pedal movement. Shoes that are worn unevenly from side-to-side will also be impossible to adjust.