For radiator support, are you referring to the tube for the starter handle?? If so.. Jensen didn't remove these. They were delivered to Jensen from Pressed Steel deleted from the assembly. (MK1a on) Kind of like the box for the battery and the spare tire support. These were never fit to a Tiger body shell. Pressed steel built the Tiger and Alpine shells on a different line. That way there was less waste, and the cars could be delivered to Jensen and less was required there as well. Pressed steel delivered the cars without the "top hats" installed and no trans bulkhead and tunnel as well. That way Jensen could just lay out a template and make the gas cuts in the firewall and floor in prep for the new parts. Again, less waste.
The Mk2 Tiger shell definitively shows that there was a separate line for body builds as the rear shelf pressing for a Mk2 Tiger is from the Hillman Husky, and the Alpine rear shelf pressing continued on as before with the battery box. It would have been way too much work for Jensen to have made that modification.
A good general guide about who did what is in the type of welding. If it was brazed (MK1 radiator mounting bungs) or mig welded (everything else), it was Jensen. If it was spot welded, it was Pressed Steel on the initial body assembly line..
The primary reason for the deletion of specific parts on shells that were destined to be Tigers was that these cars were painted before they went to Jensen. Pressed Steel and Rootes wanted a minimum amount of paint rectification as possible.