A good used 0.030" differential shim Jaguar part number 3938 or 4HA-049 (item 10 in the illustration) this has recently been removed from a Jaguar MK2 rear axle and will pretty much fit all the differentials in the classic Jaguar range with 4HA axles.

Measures 0.030" with my uncalibrated micrometer.

Reproduction aftermarket  items are available for about £1.58 or Genuine Jaguar ones are just under £4.00 from SNG Barratts.