Highly recommend you look into this:
as it has something for everyone, regardless of whether their interest is History, Dickens, Shakespeare, Theatre, Jack the Ripper, or whatever.
When I've been there, they were presented by what I was told were folks from the theatre – they could speak loudly, clearly, and with the sort of storytelling that you don't get from typical tour guides. Typically ended at a pub.
Check Covent Gardens as they have discount tickets for theatre shows – if you aren't picky, you can get great deals on tickets for that night's shows that haven't sold or aren't the best seats in the house. Always a number of different shows, from comedy to drama to musical to whatever. If The Reduced Shakespeare Company is performing ANY of their shows, make it a point to see. Laughed my ass off at each of three different ones I've seen through the years.
is but one of the sellers that do this.
Private Matters recommendations are quite good – recommend both Warwick (pronounce it as Warrick or they know you are a furriner) and Stratford on Avon – Slug and Lettuce used to be a great pub there.
If you can, and you need to book before you go, IIRC, the locking up ceremony at the Tower.
If Harry Potter fans, this might be of interest:
If they like a bit of "cultured dining" a high tea at Selfridge's or elsewhere – book in advance
Piccadilly Circus at night to see the lights and people watch.
Hyde Park on Saturday mornings used to have both artists selling their works as well as soap box speakers on a variety of topics. I locked horns with one who was apparently used to bullying certain members of the public walking by and I think it was a new experience to have someone who could fire back harder than he could dish out.
Portobello Road Market on Saturday AM
Among all of the interesting shops, if you look, you can find the location of the place that was supposed to be the travel book store from Notting Hill, the ACTUAL travel bookstore at Notting Hill, the Blue Door where Hugh Grant supposedly lived nearby. Right by the actual travel bookstore is a great spice shop.