Train Sim World 2

From the main menu select London Underground and then Explore and Explore on Foot. (Making sure you select 1938 stock)

Select whichever weather you want and you can then select your time and starting station.

Choose 07:10 and start at Harrow and Wealdstone the 1938 stock will arrive within a minute. Sit as a passenger and you will arrive at Elephant and Castle which is the last stop a while later (about an hour) the progress on the achievement should be at 62%. Restart the game from the start menu and redo it. The achievement should then unlock in the tunnel just before Paddington Station. All together this should take about an hour and a half.

Alternatively you can wait on the service at Elephant and Castle and the train will continue back to Harrow and Wealdstone. Thanks to Jobbenar for the information.