The four of us (two adults, two then teens) plus large suitcases each and carry-ons/back packs easily walked from Kings Cross to the next station on our first trip to London. The architecture along the way makes it a very interesting walk. (We arrived via train from York to discover an emergency had closed King's Cross tube station.)
If you are at King's Cross rail station, do look for platform 9ľ.
Not all tube stations will be closed all the time. Here's what the Tube has made available online now for planning:
London Tube during the Olympics
But as
Mithalwen said to me, London is very good at moving large numbers of people efficiently.