The behaviour you describe is called "hunting"; it's typical of an engine with an over-lean fuel:air mixture.

Check the inlet manifolds as there is an air leak somewhere; typically it's a loose joint, faulty gasket, or a cracked or corroded manifold, do not expect to be able to see any cracks with the naked eye as they are usually barely perceptible hairline fractures.

The brakes are servo assisted and use the lower pressure air in the inlet manifold of the engine when running, so when you use the brakes it puts an additional load on the inlet manifold and forces any intake leaks to allow even more air into the system. This will cause the fuel:air mixture to become far too weak to sustain combustion and the engine will stall.

You'll save yourself a lot of time and headaches if you get the car to a garage which will be able to quickly and accurately diagnose the fault for you. Then you can choose whether to have them make repairs or to do so yourself; if you choose the DIY option then the garage will reasonably expect a payment for the work done to diagnose the fault.