Hi,
Typically, common black undercoating was not used. If you find it on a TR, it was probably sprayed on by a dealer or a previous owner.
On complete disassembly of my 1962 TR4, I did not find undercoating but did find *a lot* of what appeared to be Waxoyl underneath, in and around parts.
This is a semi-transparent rust preventative/protectant. It's basically the same stuff still used to protect engine compartments, chassis and suspensions, especially during overseas shipment when the cars would be sitting inside the hold of a ship and exposed to a lot of sea air. When I worked at a dealership in the early 1970s, we basically steam-cleaned the stuff off the obvious areas as a part of the final prep before customer pickup. But, a lot was left in the nooks and crannies, and under the car.
Around all the handbrake linkage and the differential of my car, Waxoyl was sometimes 1/4" or thicker. The handbrake lever mechanism was completely encased in it. And it did its job... underneath the stuff the parts were pristine.
There are spray-on undercoating removers available from auto paint suppliers and restoration shops. I know Eastwood Co. sells it, although you might find it at a lower price elsewhere. It's still not an easy job, but this probably the safest method.
A preliminary steam cleaning might help. Just be sure to get everything totally dry as quickly as possible to prevent any increased or new rust problems.
I've used a propane torch myself, to soften undercoat, but I don't recommend it and it needs to be done *very* cautiously! A heat gun might be a better choice than a torch, but still needs to be used cautiously. Be especially careful around fuel lines and brake pipes!
No matter what, you'll find yourself using a putty knife and spending some quality time with the car!
Cheers!