That tea may outlive the House of Windsor is not so scandalous a statement as you might suppose. It is entirely possible that Charles, when he ascends to the throne, may declare that his name as King be "George VII" or "Edward IX" (not likely "Charles III," the first two being somewhat infamous) and the name of his house as Mountbatten (after his father and favorite uncle) rather than Windsor.
That tea may also outlive the monarchy, though perhaps scandalous, is looking more like a reasonable possibility. Confidence in the heir to the throne, Charles (Prince of Wales, Duke of Rothesay, Duke of Cornwall, Earl of Carrick, Earl of Chester, and Knight of the Garter), continues at an all-time low. Recently, the noted periodical The Economist came out in favor of the United Kingdom as a republic (that is, a non-monarchy -- nothing to do with American Republicans). "An Idea Who's Time Has Past" 333 (n. 7886) Economist 15 (Oct . 22, 1994); "Bagehot: On The Monarchy" 333 (n. 7886) Economist 71 (Oct. 22, 1994). Not to fear, however, the British royal house has survived many such onslaughts and have exercised remarkable flexibility. Even The Economist, a few months later and by invitation, published a constitutional analysis concluding that the Monarch preforms very useful and potentially vital role in the formation of Parliament. Peter Hennessy, "The Throne Behind The Power" 333 (n. 7895) Economist 77 (Dec. 24, 1994). Though the monarchy be threatened, it is not destroyed.