I am under the impression that the Queen and immediate members of the Royal family are exempt from tax, and only pay it voluntarily...so why would they have needed to exempt the jewels from tax by donating personal property to the State?
I think that used to be the case, but my understanding is that the Queen does actually now pay taxes on her income and capital gains, and that this change was effectuated about a decade ago.
I believe this agreement was made after a general uproar from the public following on the heels of the Windsor Castle fire, royal marital scandals, costs of the yacht
Brittania, etc. Robert, can you shed any light on this?
As far as the rest of the British royal family, I believe that individual members still receive payments from the Civil List, but by agreement with Parliament, the Queen now reimburses the Treasury from her own pocket for payments made to her family members (but can claim said payments as a tax offset, e.g., deduction, so she actually benefits in a way).
I
think this is the current state of affairs, but am certainly willing to stand corrected, since UK tax law is not my area of practice.

Jane