Generally brakes that slowly apply themselves as the car drives are caused by a bad booster.
The principle behind a booster is simple. It’s a canister with a diaphragm in it through which traverses the brake rod. Your pedal is on one end of the rod, behind the booster, and the master cylinder pistons are on the other end of the rod, in front of the canister.
When the system is static, a valve in the diaphragm assembly allows the pressure/vacuum on both sides of the diaphragm to be equal and the canister sealed off from atmosphere, leaving the diaphragm just sitting. When you brake, the aforementioned valve allows the vacuum from the engine to pull the diaphragm forward when you brake while venting the rear surface of the diaphragm to atmosphere, helping you apply the brakes. When you release the brakes, the diaphragm returns to it neutral position, the valve assembly seals the entire canister and allows the entire canister to equalize, stopping the diaphragm from doing anything useful.
Constantly increasing brake line pressure is generally a failure of the booster valve assembly to completely seal the canister and allow the pressure/vacuum on the diaphragm’s front and rear surfaces to equalize fully. As the diaphragm slowly pulls the brake rod forward, the valve assembly begins to operate as if the brake were slightly applied.
Perhaps the most definitive way to test this is to clamp off the vacuum line to the engine. It needs to be clamped to prevent the engine from experiencing a vacuum leak. The brakes will be very firm without the booster assist, so do this test carefully. If the problem disappears, it’s the booster.