Steve: Good post. Just to reiterate that the Visit Britain website includes neither Buckingham Palace, Windsor Castle nor the Tower in either top ten. Though I must say, you did forget the Beefeaters... :-

Nice of you to iterate. But you haven't given a link to your source. Yes 'Visit Britain' can be searched, and their list of attractions is Here
Not only is it false to claim that The Tower doesn't appear, it is listed as No1 in the 'paid' attractions.

So your best shot is Buck House at number 11! And we've had this thing about the Tower of London before, haven't we? Would you care to tell us when it was last occupied by any royal? 1603 apparently

Shifting the goalposts?
hardly any of the "royal assets" ever make the top twenty tourist attractions in this country.

There is a difference between 'royal assets' and assets 'occupied' by royals.