There’s no issue having the car in 3 weeks time. Contact motability closer to your move-in date to the property and claim the free wall charge installation.
If you are certain of the move-in date and have pictures of the consumer unit/electric meter along with pictures of where you’d like the charger installed, you can book the installation weeks in advance. This way you don’t have to wait 4/5 weeks after the move to have it installed.
I did exactly this and the installation was done much sooner.