Hydraulics that sit idle are prone to such maladies. The DOT3 and 4 fluids become corrosive to the metals in the cylinders because they are hygroscopic (they absorb water out of the air). Your brake and clutch components are essential for safety and it sounds as if an overhaul may be in order at least to the clutch (The brakes probably won’t be far behind.)
The suggestion to look for where the fluid has leaked out of is a good starting point. If its on the floor of the car its leaking out of the master cylinder (where the pedal attaches), it will be absorbed into the carpet, but you will be able to feel it and smell it when it gets on your hands from handling the carpet. If its out on the ground, then its leaking out of the slave cylinder (where it attaches underneath to the transmission). The other leak possibility is the clutch line itself. It could have rusted / worn through. That should be an obvious leak.
Tiger Tom does still rebuild hydraulic components, although he is really busy with lots of projects. (We did a break booster not long ago.)
Its just a matter of wrenching and elbow grease to get the parts off your car to be cleaned up and restored to working order. Log into the Members Only section and review Section K of the Sunbeam Survivor Manual. https://www.teae.org/member-login/
Nothing to be afraid of, just don’t round off any fasteners, and use the right spanner for the application. No real damage can be done other than those pitfalls. Once they’re off the car (clutch line included), they can be dis-assembled and flushed out (by a pro if needed). Then the inspection can be done to see if its a failed seal, corroded cylinder bore, etc. Something is obviously blocked, or it would flow freely out of the bleeder screws.
This would be a good opportunity to switch to a DOT 5 silicone fluid in the clutch. (Throw your tomatoes now, I still love DOT 5.) It won’t strip paint, and won’t corrode especially if the car sits in storage a lot. You just can’t use the vacuum bleeder with DOT 5.
British cars have been making mechanics out of ordinary men for years 🙂