The CF prefix indicates that it is a 1973 model carb spec car. The prefix CC was used on carb spec cars for the 1969 through 1972 model years. The production survey information that I have shows that there was an overlap of about 20 days when both CC and CF series cars were produced covering mid September through early October. If we operate on the assumption that the production date information posted above for CF2365U, your car was also produced in October of 1972. Taking a proportional number of days from the date of CF1U build and with CF4029U being the first CC series TR6 built in 1973, no more CC series cars on the line after early October, thinking about holidays and all that plus the chassis number of the first TR6 built in the 1973 calendar year, I'd guess that it was rather late in October for the build date. As for using the CR series car above, you can't really do that to try and date production of your car since the CP and CR series of PI cars changeover dates differ and they carried their own list of serial numbers with CR6701 being the last PI car produced in early 1975 while the last of the TR6s (CF58328U) was built in mid July of 1976.
Looking at the CR series car linked and thinking about the serial number of the first CR series car produced during calendar year 1973 and the date the last 1973 model year CR series car was produced, the indicated BMIHT build date listed is right in line with any guess I would have made regarding build date using number of cars and number of working days to make that guess. Since that car carries an "O" suffix, it is/was originally fitted with an overdrive transmission.
As for the "U" suffix used for calendar year 1972 and up vs the "L" suffix used for calendar year 1971 back, I believe that the "L" was used to designate left hand drive cars going back to the TR2/TR3 days with no letter designation being used for right hand drive cars. BMC on the other hand had a habit of using "U" as a designation in their serial numbers and I can't help but wonder if the change was a reflection of all the bits that came together to form British Leyland entering into the mix.