While my favorite companion in Fallout London is Churchill the dog, I have to say Mad Jack is among the most interesting companions to have.
Unlike Kiera, recruiting Mad Jack is not tied to any story quests in the game. However, you do need to complete a side quest near the Trafalgar Square.
How To Recruit Mad Jack In Fallout London
Travel to The Pilgrim Pub which you can find northwest of Trafalgar Square. The pub in question is located in the basement area, so you will need to enter the building to find Mad Jack.
When inside the pub, speak with the manager, Jack Nesbitt. He will introduce you to the underground fight club that takes place in the basement where you will meet Mad Jack himself.
After the introduction, you will be prompted to fight Mad Jack so agree to fight by choosing “No offense but I think I can take you for a minute in the ring” dialogue option. Do not attack him until the manager has finished his introduction; otherwise, it may not work.
The fight will last for 60 seconds. You need to survive this time while dealing damage to Mad Jack.
Once the timer runs out, if you’ve managed to survive the fight, Mad Jack will be impressed by your abilities.
After the fight follow Mad Jack into his office and speak to him about joining your party as a companion. Keep in mind that your current party member will be dismissed and right now there is a bug with Kiera and Churchill that makes them permanently disappear when dismissed.