A friend of mine from Girl Guides is working at the railroad museum in York, she really loves it, that might be a fun option. Recently (last week) I took a trip back to the last state I lived in, and rented a car for the 1st time. I actually did not really enjoy the experience, the car was way more automated and locked by itself when I didn't tell it to, and had several seat adjustments they didn't tell me about, and I had to use a lower gear to avoid a new feature that cuts the engine out at red lights. And I really knew the area, and had only hopped on a train for 3 hours. I turned it in after only 1 day, it wasn't covered by collision, and would have cost much more than taxis, so I bailed on it.
I might like to drive my brother in law's car in England someday, around a parking lot to try out the idea of driving on the older, left-side of the road. Otherwise I can't imagine having to depend on that car rental experience for my "vacation." I would NOT feel relaxed with dealing with all that stuff when I had no need to. If I had someone else with me who was feeling stressed out about it on top of the un-fun experience, I would never have done it for a day.
My Dad lived in Australia part of the year for a decade+, and when he came back here to drive on our side of the road again each year, it was a challenge for several days, and he was a VERY experienced driver, often going across country in his camper van. The blinker being on the other side of the steering wheel was one of the big challenges, so he'd hit the other stick too, and turn on the windshield wipers at the same time, to be sure he had his directional signal on.
Realistically, it's a great thing to treat yourself to the very most FUN trip possible, and to delegate as much of the chores as possible, I find riding overground trains and buses is a huge way to reduce stress and to see the sights.
Also I choose hotels in London which have some breakfast attached so the stress levels for the day start out low, then I can forrage later on for lunch or dinner :) Sometimes just finding a little store or cafe' for breakfast is a big challenge. I always go as low-stress as I can, and during most all the trips I've taken to London over the years, I've used only the buses (tube has very fast, very steep escallators and I have some double vision, buses are easier, you step up and poof, you're there), and have had great trips, sometimes need to call a taxi to save me from a planning mistake/lack of info.
If there's some really important photo op for one of your group that is not on an easy train line, require that person to plan the ENTIRE section of that trip. If they see it's really difficult, and if they see it will require them to drive on the left, they may think better of the idea, at least on the 1st trip. It could be something relegated to a 2nd trip.
Chelsea Flower Show happens in London in May, you might want to get some tickets for that if you can. :)
There's a zillion things to do in London without flowers, but just a thought :)
Have the most FUN possible!
-Alison