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? And please don't regale me with the fact that it's the shameful home of the disgusting Crown Jewels...

As for the most popular, it's depends on which website you look things up. The Visit Britain site gives two top ten lists, free ones and paid ones. No royal attraction makes it to either list, not even the Tower if you really insist on having it as a royal attraction, which I heartily dispute. And that website does it by numbers of visitors, not by someone's subjective opinion.