Walk forward and you'll meet Stachen. He'll say that he knows we've gotten into some trouble. Is he foreshadowing something? Check the door to enter the clock shop. Spring will tell you that Cogg is still in the back room. Move forward and talk to Cogg. Just as he is about to activate the time machine, Inspector Chelmey, Barton and Flora all barge in, having secretly followed Layton to the shop. However, Cogg has already started the machine, and it transports everyone in the shop into the future!
The more the merrier[edit]
Having travelled 10 years into the future, everyone is a bit worse for wear. Inspector Chelmey and Barton will set out to investigate, while Flora is so dizzy she almost faints. Move out of the clock shop. Talk to Inspector Chelmey, who quickly gets over the shock of ending up in future London. He wants to find the prime minister with Barton, and doesn't want Layton participating in the investigation. For now, however, there's a very out-of-place for us to get. Talk to Cogg to travel back to the present, then move to 
Gresenheller U. Talk to Rosetta for Puzzle 134. After doing so, go back to the future, outside the clock shop.
Talk to Art for Puzzle 053, which will net you the 
trowel sticker. Move back and talk to Stachen, who mysteriously didn't age since we last saw him. He will request some mushrooms to be delivered to him, giving you the 
Stachen's Toadstool errand. Once you've done so, enter Anita's Place. Talk to Anita for Puzzle 054. Talk to Alfie for Puzzle 135, which will net you the 
Chef sticker. Exit the café.
Return to the hotel[edit]
Move back twice. Talk to Adeline for Puzzle 055, which will net you the A Flower for Adeline errand. Move to Southern Street, then talk to Minnie for Puzzle 137, which will net you the Minnie's Homemade Cake errand. Enter the hotel, talk to Becky and go into the hotel room. Layton will now explain their current situation to Flora.
She seems to understand most of it, but questions why we've yet to see the future counterpart of Flora. Go downstairs and talk to an aged Delmona, then exit the hotel. Enter the arcade and talk to the Family Goon for Puzzle 056, then enter the restaurant. Talk to Paillard for Puzzle 057, which will net you a 
milk sticker and the Paillard's Tomato Supreme errand. Talk to Shipley, who teels you that Luke is waiting at the observatory in the park north of here. Exit the restaurant.
Reunite with Luke[edit]
Move forward and talk to Inspector Chelmey, then exit the arcade. Move north and west to the park, then check the door to the observatory to trigger Puzzle 058. Once you're inside, talk to Luke. He will say that he needs a way to lure the guards standing at Chinatown's gate, and that the only way they will move is if future Layton tells them to.
Future Luke will state that Layton almost never interact with low-level thugs, instead having his orders conveyed by his lieutenant, Bostro. He will suggest that we use the parrot we befriended to learn Bostro's voice, then have it yell at the grunts to make them move away. He will also say that Bostro can often be found around the Gilded 7 Casino, so we'll need to investigate that area to advance.