[wilf leek]

Narrowing of Jag rear ends is commonplace here. Best way to do it is to use some heavy-duty cold drawn seamless tube of about (don't quote me) 11/2 to 2" diameter instead of the original solid halfshaft. Bigger area to weld to the yokes at each end, and a much stronger unit. Use of a seriously competent welder is mandatory.

Also, I am constantly concerned that users of these irs units do not tie the inner lower wishbone pivots into the frame. My own car has this done at each end of the wishbone. Thus failure of those two (and too small to my mind) bolts which clamp the wishbone pivot casting to the diff is also eliminated.
I would not drive a cobra using a jag rear end unless this is done, certainly not at the speeds I commonly enjoy.

To get back to the original question, whilst diff clutch packs can take a while to wear in, they should not lock up the rear. Has it been correctly assembled?
In a light car like your TVR, you could consider reversing some of the clutch plates to reduce the locking action - again something I recommend in a Cobra. Personally I use an open diff for roadwork - makes for a sweeter handling car. Never could understand the desire for lsd in these light cars on the road. Track is a different matter.

Just my 2p's