What a very silly article. They argue about how many millions the royal family cost (not very many, considering our total £700+ billion public spending), and they attribute things like the 'Master of the Household's Department' to the Queen, which includes spending on things like state banquets for visting Presidents and stuff which we'd have anyway regardless of the monarchy.
And then they claim that the sum total of tourism output is ticket sales to Buckingham Palace? What about Windsor Castle, the Tower of London, Kensington Palace, etc. What about the tourists who come here (partly) to stand outside Buckingham Palace and watch Changing of the Guard.
According to this article
dailycaller.com/2012/09/26/taxpayers-spent-1-4-billion-on-obama-family-last-year-perks-questioned-in-new-book/
"Taxpayers spent $1.4 billion dollars on everything from staffing, housing, flying and entertaining President Obama and his family last year, according to the author of a new book on taxpayer-funded presidential perks.
In comparison, British taxpayers spent just $57.8 million on the royal family."
Obviously numbers are exaggerated, but we still have to spend money on state boozing and dining.