I was impressed by gentlemen from STORROR (YouTube channel) for finding the shortcut from Moorgate to Farringdon to allow them to be faster than the tube on that route.
This solution is excellent for commuters who just miss the train at Moorgate, and they are desperate to catch it. For example, because it is Fast Chesham service that is only every 30 minutes. In that case, simply follow the route shown below in the video. Its worth to mention that basic knowledge of parkour may come handy while using this shortcut.
Sadly with my agility of sumo fighter, I will be unable to use this such a useful shortcut :(, but I hope you will find useful.
A big respect for these guys from STORROR. Link to their YouTube can be found here: https://www.youtube.com/channel/UCdPui8EYr_sX6q1xNXCRPXg