Frostpunk: Edition

In order to have this achievement pop, you need to get your count of people intending to leave for London to zero before the timer runs down. I managed this by going down the "Faith" purpose, and constructing churches and the temple, and then using the sermon and evening prayer abilities as often as I was able.
Get your hope up as quickly as possible after the news of the other colony failure, and work on keeping discontent down.
When the number of "Londoners" hits zero, the task will disappear and the achievement will unlock.

Note of warning, if you choose to create New Order, it will null the achievement, you have to naturally make them stay not kill them (shocking!), the easier way to do this is letting the spokeperson of the Londoners speak freely three times, letting him rally the Londoners... The fourth time that happens you will be given the chance to respond and give your own speech, causing a huge drop of londoners followers... That is also the solution for the achievement.

Not a guide since I don't know how to do it, but a warning. It's actually don't let anyone try to leave for London. I got to the point with 100% hope and 0% discontent and still 7 people tried and I used guards to stop them (resulting in a few injuries and a death) and no achievement.