The way the E Type exhaust manifolds connect to the downpipes is poorly engineered. The mainfold has a threaded stud screwed into it. This thread is 3/8" UNF and the problem with the fine thread is that corrosion accelerated by heat means that the thread in the manifold fails. Then the stud strips and the exhaust leaks because it can't be tightened. Mine are full of bolts: 

I thought about a helicoil repair but this still leaves you with the delicate UNF thread.

I obtained some studs that have the standard UNF thread at one end but have a 7/16" UNC thread on the other. These are screw in rocker arm studs for short block Chevy V8 engines. Elgin part number was RD1920.

The holes needed to be drilled out and it is important that they are parallel. I made a small jig out of a piece of 1" angle iron so I could bolt the manifold to my pedestal drill.

The studs needed to be cut down 10mm on the coarse thread end to be a perfect fit. The fine threaded end is actually a little longer than the original stud. The minimum crush distance is about 0.65 " which I think will be small enough; if not I will run a thread die further down the stud.

The manifold I chose to do the first repair on was about the worst one I could find and I think it looks pretty good.

Inspired, I did another one, then cleaned them both up with a flap disc on an angle grinder and finally painted them.