Art and Don are both essentially correct. The 2138cc engine became available around 1959, as I recall. Offhand I can't remember if they got unique engine serial numbers. TR3Bs could have TSF engines (still 1991cc) or TCF engines (2138cc), and early TR4s could have CT engines (2138cc) or CTA engines (1991cc), but the latter engines were pretty rare (some cars sold in Japan and some special order cars).
Point is, though, one really can't be sure of the displacement of a wet-liner engine 40-60 years on without measuring the pistons or liners. Aside from the 83mm or 86mm sets originally used in the TR engines, there was the 85mm set (2088cc) used in the Vanguards, and even an 80mm set (1670cc) in the Standard Ensign! And in recent years there have been the 87mm and even 89mm sets for performance upgrades.