After they went shopping, they left Diagon Alley (and the Wizarding World) via wall behind the Leaky Cauldron and then back into the Muggle world. 

> **The late-afternoon sun hung low in the sky as Harry and Hagrid made their way back down Diagon Alley, back through the wall, back through the Leaky Cauldron, now empty.** 

> <sub><sup>Harry Potter and the Philosopher's Stone - — CHAPTER FIVE — Diagon Alley</sub></sup>

They traveled by Underground from the Cauldron to Paddington where Harry caught a train back to Little Whinging. In the film this journey is omitted but we do see them in the Cauldron, when [Harry learns about his parent's fate][2] at the hands of Voldemort.

> Harry didn’t speak at all as they walked down the road; he didn’t even notice how much people were gawping at them on the Underground, laden as they were with all their funny-shaped packages, with the sleeping snowy owl on Harry’s lap. Up another escalator, out into Paddington station; Harry only realised where they were when Hagrid tapped him on the shoulder.

> <sub><sup>Harry Potter and the Philosopher's Stone - — CHAPTER FIVE — Diagon Alley</sub></sup>

Several weeks later Harry then traveled from Little Whinging to Kings Cross (meeting the Weasleys) where he then returned to the Wizard World via the gate at Platform 9 3/4

  [1]: https://www.rome2rio.com/s/King-s-Cross-Station/Charing-Cross-Road
  [2]: https://www.youtube.com/watch?v=jcFd8RNqKuA