It depends which member of the Royal Family you mean. If it's the queen, do remember she's in her nineties so her choice of food will reflect that. However, she does like her Earl Grey with plain biscuits first thing in the morning, and where possible, she will avoid carbs - potatoes, pasta, rice - with her main dish. She enjoys her afternoon tea, bone china and tiny delicate sandwiches, cucumber, salmon, and circles of choice jam as fillings. These are followed by cakes.
Prince Charles, of course, emphasizes organic produce and has his gardens full of them. Prince Philip has no time for this and likes his lamb chops and other meaty delicacies. When it comes to formal dining, the menus are always in French. However, they may well translate into such items as omelette with asparagus, although this example would only be one of the starters, of course.