en.wikipedia.org/wiki/List_of_British_royal_residences
Scroll down to "Current royal residences by type of residence" to see which are state-owned, which belong to the /crown Estate, which are privately owned etc.
The Crown estate en.wikipedia.org/wiki/Crown_Estate "is neither government property nor part of the monarch's private estate"
Once upon a time, a monarch owned the whole country, granting the use of bits of it to those who had helped them win it by conquest and would help govern it. The costs of government and of funding an army to defend it and/conquer other land was met by the monarch himself from income from his possessions.
"Historically, Crown Estate properties were administered by the reigning monarch to help fund the business of governing the country. However, in 1760, George III surrendered control over the Estate's revenues to the treasury, thus relieving him of the responsibility to personally pay for the costs of the civil service, the national debt, and his own personal debts. In return, he received an annual grant known as the Civil List." Each monarch agrres to the continuation of this arrangement upon accession
"The revenues from these hereditary possessions have been placed by the monarch at the disposition of Her Majesty's Government and thus proceed directly to Her Majesty's Treasury for the benefit of the British nation."
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