You could try emailing the RS Office and asking. It may be that they use a variety of places across their trips. If they can’t tell you, you could ask on your first day of the tour and then book your own experience after arrival.
While you say that you want to do afternoon tea several times, it can be very expensive (50 pounds a person or more at a fancy place) to do the full afternoon tea with sandwiches and baked goods; it is a lot of food. I’ve only gone to afternoon tea once (at Brown’s Hotel) in many years of travel and a year of living in London. It is a nice experience, but not one that is done on a frequent basis. If you are just looking for a cup of tea and a snack, there will be many places you can take a quick break (e.g., museum cafeterias, bakeries, etc.)