I've just noticed my old thread, so I wanted to come back and thank you all for inspiration.
We went in mid June, luckily before the main heatwaves. I'd prefer May, but health issues made us postpone.
Thanks for the tip for the Wetherspoons. That was what I needed for food - not a high cuisine, but a solid predictable food, beer and lemonade and easy to find wherever we went.
We walked around the historical sites (it is oddly comforting to know they look exactly as they did in my first English textbooks), but didn't went inside - the mood was that we do have large medieval castles and churches at home. Plus, westminster area was so crowded that we cut the walk short there.
What we don't have at home are that impressive high-rise buildings - we got to the Horizon, Garden at 120 and breakfast at Skygarden, and taking DLR from Greenwich lead to an extra walk at Canary wharf area.
We liked the parks as well.
The Thames boat trip worked well - enough to look at for everyone, and than we've sit at the Garden 120 the next day, looked at the route together and translated some highlights from the comentary.
In the end, my parents prefered more time outside, to just see more of the city while the younger ones took turns to separate from the group and check museums and exhibitions (Natural history and Maritime museum, HP studios).
Looking back at it, the preferences made sense - the younger members speak English and visited US/Canada before, so wanted the London-specific stuff and a bit deeper look, while my parents used it as a way to see a bit of anglosphere life in general with the cultural mix, skyscrapers, plus seeing the main sights.
Overall, it was a great trip, thanks again, this thread helped me with choosing the right plan for us.