The exhibition is being staged by a charity (The RCT) and I believe you can be sure that the Royal Family will not benefit in a pecuniary way from any surplus from the event which you mention.
Yes £22 is a lump but not out of line with the cost of many similar events especially in the Capital. You didn't mention the list of reductions which taper down to just £1 for recipients of certain benefits.
Personally I don't see the Royals in the way you describe them although in every family there are wrong'uns.