Most of the personal income into the household is through the Royal properties. There are extensive farming lands leased out. The tourism you mentioned would be similar I think. Also, the islands of Jersey and Guernsey off of France in the English Channel and I think Isle of Man in the Irish Sea are royal protectorates completely separate from Great Briton.
As I understand it, the several places in London are used for State functions so costs for operation and maintenance are shared by the government. In addition, when royals are engaged in anything thing government related, the royals are essentially on a government expense account so to speak.
Feel free to correct anything where you have better information than I.
There’s a reason they refer to themselves as “The Firm”.