Wow - you prompted me to do some research - and wow. Pricey. The Black Taxi Tour company, which looks like the OG, offers a “classic London sights” tour of 4 hours in length for £408. That price is per cab, and up to 6 folks can be accommodated. They do have a huge range of options! But £408 looks like the cheapest they offer.
Echoing Claudia, I find London extremely walkable. And there is so much packed into every square kilometer that you can never run out of new things to discover!
For short distances and for sightseeing, I am more a bus than a tube person, and lo! TFL has a section on their website dedicated to “leisure routes” on their iconic double decker buses: https://tfl.gov.uk/travel-information/visiting-london/experience-london/bus-leisure-routes - the bus is cheap! You can see things! And if you want to meet a local, just make a comment about the traffic or the weather and you’ll be off to the races!
On the other hand, if you have the scratch, some of those cab tours look pretty fun. :-)
You can go to the Cotswolds, do a Beatles tour, a Taylor Swift tour, American heritage, Bridgerton (in London or in Bath), James Bond, Jewish East End, and many many more. Impressive.