I'm guessing that some long-ago owner simply got confused(?) on the year of the car. Supposedly the very last 3A was TS82346 or possibly TS82347, and the very first TR3 built in 1961 was TS82030, so TS80897L would've been built probably sometime in the second half (or maybe closer to the end of) 1960. Regardless, production of the 3A had trailed off rapidly by the end of 1960; in 1961, only 408 were built, and a further 7(!) in 1962 (not counting the 3B series). [This information is from Bill Piggott's latest Collector's Originality Guide.]
Edit: The car looks nice enough, so long as the bonnet stays down. Inside that engine compartment it looks like a $500 special. How people can spend that much on the outside and interior and "cheap out" with a rattle can of flat black under the hood is beyond me. (Oh, and it's the wrong voltage regulator...which also is mounted wrong for a post-TS60000 car!)
Edit, part 2: Gordon, I must have been typing while you posted!