One of the issues with replacement air conditioning system parts for all BL cars of that time except Jaguar is that the cars came without a factory installed air conditioning system. Essentially each dealer installed whatever system they had decided to use so the first step may be to determine the air conditioning system manufacturer. The "official" BL air conditioning systems for Austin, MG and Triumph were under HACxxx or HACxxxx series of accessory part numbers and were made by Mark IV Manufacturing in the northern reaches of Fort Worth. There were two Austin/MG dealers in Dallas, one used the BL kits, the other used a different aftermarket kit made in Grand Prairie TX (seem to recall that it was ARA but not be sure of that). The lone Triumph dealer in Dallas County mostly used the BL kit but were known to use the kit from the outfit in Grand Prairie if the BL kits were on back order. Mark IV is long gone, sold to Volkswagen to make A/C system components and kits under the Volkswagen Parts Corporation umbrella and as air conditioning systems from the factory became essentially a standard, that part of VPC went away. As far as I know ARA is still around, they may be able to help.
Having said that, other than bracketry and evaporator housings, perhaps the evaporator and condensers themselves, most of the parts were commodity items. All of the period systems that I have seen used a 9 inch York compressor, off the shelf receiver driers, expansion valves, fans, fan switch and temperature switch. As a result, there is a reasonable chance that compressor bracket or set of parts making up the compressor mount system for a TR6 might work. The caveats would mostly come in with respect to specific year models and the emission controls fitted to the engine.