Last year in New York we learned that two stations that are shown as connected on the subway map may in fact be connected by a long and unpleasant walk.
I'm thinking that in London, one might want to avoid changing lines at Paddington, King's Cross, Bank/Monument. and a few others.
Our two runs with large backpacks will be Victoria to Hounslow West, which shouldn't be too bad, and Paddington (from the train) to Victoria (tube station) which might be tricky.
Any advice will be welcome.