need activity ideas for MiM > Paddington > LHR hotel transfer day

Paddington station is a 15 minute walk from Hyde Park or a quick taxi ride. If your legs object! The Victoria and Albert Museum is on the other side of Hyde Park from Paddington so you could get a taxi there. I love seeing the V&A. You could have lunch there too.

I hope you will write a trip report about your walk on the Cotswolds Way, I have thought about doing that.

Given that you don't want to do much walking, how about the Alexander Fleming Museum about 100 m from Paddington station.
https://www.imperial.nhs.uk/about-us/what-we-do/fleming-museum
Then you could have a meal in the Market Halls
https://markethalls.co.uk/

The Fleming museum is worth a short visit, but there's not that much to see there.
It won't take too long.

On the other side of Paddington, Little Venice is a nice place to while away some
time and be a bit away from the hustle and bustle of the rest of London.

Given that you say it's your first time in London, but are not sure if you want to
walk that much, maybe a concert of some kind? If your legs are up to it, of course,
there are a multitude of museums and strolls to enjoy.

I would hope/guess that if your hotel is near Paddington, you could stop there
and they would store your luggage prior to being able to check in.

Their hotel isn’t near Paddington, but at the airport. It would certainly be a much easier and fun day if they were staying in London that night and then going to airport next morning for the flight.

In terms of luggage storage, I used both the Bounce and Stasher apps recently and found storage that were very conveniently located for our plans.

A Google AI search pointed me to the 23 bus which departs from Paddington and then if you just get off and then reverse the route takes you back there. Double decker and goes past some landmarks such as Piccadilly Circus and Trafalgar Square. Buses are tap and pay with contactless credit card in London so you don’t need any special transit card. You can store your luggage at station for the day.

Here’s the complete 23 bus route. https://tfl.gov.uk/bus/route/23/

Assuming you can stash your bags at Paddington, how about getting the Elizabeth Line to Liverpool Street station and then a number 26 bus towards Victoria from just outside. This will take you past a number of major landmarks including Big Ben and Trafalgar Square. Perhaps you can get a taste of London if you’ve not been before. You can get the circle line from Victoria back to Paddington

This is a regular bus and you pay (like the trains in London, but not the train from MIM) by tapping a credit card as you get on. It’s worth going upstairs and trying to get to the front for the best views.

There are Hop on, hop off buses going past the main sights but these are regularly criticised here as being very slow. I have never used one, but they do seem very expensive.