Given that the cars were made for both LHD and RHD markets the conversion is relatively straight forward. For example, there is a pressing on both sides of the car on the firewall where the steering column goes through.
You can use the LHD pedal box and the brake cylinder but as Malbaby found, you need to mount the clutch cylinder on top of the pedal box, not on the front where it causes clearance problems with the carburettors. You will also need to modify the clutch pedal (or find a RHD one) and run new brake lines. A good panel beater should be able to help with the panel work needs to mount the pedal box and clean up the holes on the left hand side. You will also need a new accelerator linkage.
As Triumph used common parts on so many cars, you should be able to source a steering rack. I vaguely recall that you can use a Triumph 2000 one but you need to use the correct length tie rods. Alternatively, Revington is selling brand new racks. By the time you get an old one rebuilt, that may be a better option.
I made a template out of ply to mark identically around the glovebox and the instrument mountings on the dash panel. I then cut them out with a jigsaw and had a friend weld them into place on the opposite sides. You need to make sure that the cut out picks up the steering column mounting bolts under the instruments. The welding needs to be strong but not pretty as it is hidden by the wooden dash. Unfortunately, you will need a new wooden dash.
If you are not already a member of a Triumph club, it might be a good time to join. You never know what people have hidden away in their sheds! Good luck.