I'm not sure of the TR4 tappets, here is a bit of info stemming from my research and testing of TR6/Spit tappets.
The Spitfire/TR6 requires a dead flat lifter face. The camshaft lobes are ground with zero taper. Rotation of the lifter is achieved only through the offset of the lifter centerline in relation to the lobe. It is quite possible that this is the case for the TR4 as well.
A while ago I conducted a lifter survey of the TR6 lifters, including two NOS (New Old Stock) lifters I had on the shelf from 35 years ago. Here are the results:
(EDIT: Sorry for the image, but I couldn't get the table to show correctly as plain text in the message)
"A" and "B" designations are different lifters (either different brand or
different all together) from the same supplier.
Radius is given in inches.
All of these TR6 lifters being ground very convex is one of the reasons for the high rate of failure over the last few years coupled with individuals building street engines with excessively high valve spring rates.
You'll note that even the used lifters have wear, I knew that one of them
had pretty severe wear, and I could see it. But I don't know the full
history of that motor, the used lifters were pulled randomly from two
different parts engines in the shop. But one thing that is consistent from
the used and NOS lifters is the trouble Triumph went through to polish the
lifter face to provide a very smooth surface finish.
It seems Triumph was rather unique in their approach to grinding tappets dead flat. MG T Series lifters were also ground flat, but even Austin MG changed their approach on this matter and for instance the B Series tappet should have a 32in radius.
Kai @ Wishbone Classics