It's interesting, I would have to say on average, of the BritishL1A1's that I have ether owned or passed though my hands, most have had hand stamped TMH's, very few were done via the engraving machine (with the oval slot). At what level (Unit Armourer perhaps) would hand stamping generally be employed in the British system?
The only LithgowL1A1 I ever saw re-stamped (Machine restampted), was an ex NZ Lithgow 1961 dated rifle with a replaced new build receiver.