Sunrise and sunset times are here:
https://www.suntoday.org/sunrise-sunset/2021/june.html
Calculating the difference in hours, minutes and seconds between sunset and sunrise the next day gives the NIGHT length. By chance, the nights of 20th/21st June and 21st/22nd June are the shortest at the same length of 7hrs 22mins 1sec (to the nearest second). After that the nights start to lengthen again. "When the nights start to pull in again" is therefore the following night of 22nd/23rd June at 7hrs 22mins 7sec.