It could be the spring in the master cylinder that closes off the line to the fluid reservoir. If the spring is broken, as happened on the clutch master cylinder of my Triumph TR-3A, which uses the same Girling master cylinder as on your Healey, way back in 1963, fluid will be forced back into the reservoir, instead of to the brake calipers/wheel cylinders, when your step on the brakes. I was told back then to use two springs, which will guarantee that breakage of one of the springs will not cause problems. The spring is highly tempered and very brittle, and can break without warning. I had to drive all the way from New York City to Washington, D.C., with a clutch that would not disengage back then. I forced the gearbox into fourth gear and stalled the engine every time I stopped. I then restarted the engine with the gearbox in fourth gear and the good, old, tractor engine the Triumph had drove right off. Try that with any modern car with a manual transmission.