London/southeast England and Paris

Would wasting a day come from not walking, or visiting any museums or other sights where you might sometimes be standing, and not just moving? Check out the itineraries offered by London Walks https://www.walks.com/ . They have such a variety, you should be able to find one or more guided walks that will be of interest to all of you.

For tea, look no further than Fortnum and Mason, on Piccadilly. Their afternoon posh tea is in their Diamond Jubilee salon, but they also offer a less fancy (and lower priced) tea in their Parlour.

Taking a walk is a good idea as you are likely to be tired. Personally, I wouldn’t go for one of the most expensive afternoon teas you could buy in London when you are tired and may not appreciate it.

Near South Kensington are the Muffin Man Tea Shop, La Brioche and Dishoom for good food.

Walk through Hyde Park and Kensington Gardens. See Kensington Palace.
This is how I spent the first afternoon of my first visit. Though not by design, I would still recommend it for at least part of your day if you're looking to walk.

My recommendation would be the same as the one above. Drop you bags at the hotel ( presumably they will allow this) and wander around Hyde Park ( Rose Garden, Princess Diana Fountain, and Lido of the Serpentine);and Kensington Gardens (Palace, gardens).

There are at least two cafés in the park. One is the Setpentine Cafe on the Lido ( swimming area).

https://www.royalparks.org.uk/parks/hyde-park/food-and-drink/serpentine-bar-and-kitchen

We like the Magazine Restaurant in the stunning stunning Serpentine Galleries building designed by Zaha Hadid:

https://www.serpentinegalleries.org/visit/food-drink/

You can get breakfast there until 11:30 am, or order from the regular menu after noon.