The production was allowed to film at the entrance and in the foyer of the actual Royal Court of Justice in London. This is the only movie in recent times that got permission to do so.
The Children Act is a piece of British legislation dating to 1989 that puts the welfare of the child before all other considerations, including the wishes of the parents or religious considerations.
The book Jack is reading to his nieces is called "The Daydreamer" and is written by Ian McEwan, who also wrote "The Children Act", upon which this movie is based.
This movie was based on the 2014 novel of the same name by Ian McEwan, who also wrote the screenplay.
Despite only including one use of strong language (which is usually acceptable at "PG-13"), this movie holds an "R" rating in the U.S. - likely because of the somewhat sexual context of the line in which that language appears. This is the highest rating this movie has received (requiring that children under 17 have parental accompaniment), with Canada's "14a" coming the closest.