It depends on what kinds of shows your group likes. Our group prefers (for the most part) mysteries or farces in smaller theaters; we've enjoyed pretty much every one we've been to. Also, Agatha Christie's "The Mousetrap" has been playing since I was 14 years old, and yes we did get to take our kids to it.
Our teens and tweens liked pretty much what we did; the National Gallery, Cabinet War Rooms (excellent), British Museum, Tate Modern, Tower of London. Sir John Soane's house is a little creepy and very intriguing.
Look at LondonWalks; I've liked every walk I've ever taken with them. When our son was 10 and very much into spies, we did their "Spies and Spymasters" walk, which covered both Kim Philby and James Bond (and Ian Fleming); years before that, right after I graduated from law school, I very much enjoyed their walk through the Inns of Court.
If you want to partake of an English afternoon tea, without a high price (or if some people in your group don't want to have tea), go to Richoux, a chain with several locations in London. You can get afternoon tea or other food.