Rule 1: Don't believe the Daily Mail
Having said that, every year when MoD realises that they're not going to get all the money they need to do everything the Government wants it to do, they ask each service to draw up a list of things to cut in order of priority. Somewhere on that list will appear the Battle of Britain Memorial Flight, the Red Arrows, HMS Victory, the Royal Yacht*, Household Cavalry etc. Invariably someone in the press will see the list, put two and two together and get five by assuming it's a list of what is going to get cut, not just a list of options.
*At various times the people doing the cutting have forgotten that the lists are drawn up in order of priority and cut stuff that shouldn't have been...