I don't think it's a 'skewed' sense of distance, just one that doesn't match your own. If towns and cities outside of London had the same transport links that London did, people would probably get the tube instead of walk 20 minutes. I really can't see why you'd expect people in London to walk for half an hour when there are various kinds of transport that can get you there faster?
And no Londoners I know would get the tube from Covent Garden to Leicester Square, that's what tourists do.
From my house to uni is about 35 minutes walk, the same as from my house to school was outside of London. But why would you walk 35 minutes when the bus can get you there in fifteen, or the tube in five? I guess if you were hard up on cash you might, but most people in London have a travel card of some kind, so it's irrelevant.
Also, I know plenty of people outside London who only live about a half hour's walk from their work, and they take the car every day. I don't think I know anyone who walks to work. Likewise, my parents and most of my friends live about half an hour's walk from the town centre, and they'd never dream of walking to go shopping. So London actually isn't any different, except rather than drive, we use the tube/bus.