There's a handful of stations on the tube where above ground they're but a few minutes walk even though underground the train takes much longer (and I believe I much more circuitous path). IIRC you can actually jump out at the platform and run above ground to the next station before the train arrives.
Edit: Here's a guy racing the Circle Line from Mansion House to Cannon Street https://www.youtube.com/watch?v=PH_Z8Ghuq6E