For context, I'm going to put some info from Wikipedia on Branagh here.

Kenneth Charles Branagh was born in Belfast on 10 December 1960, the son of working-class Protestant parents Frances (née Harper) and William Branagh…In early 1970, at the age of nine, Branagh moved with his family to England to escape the Troubles; they settled in Berkshire, where Branagh grew up in Reading and attended Whiteknights Primary School and Meadway School in Tilehurst…

At school, Branagh learned to speak with an RP accent to avoid bullying. Discussing his identity, he later said, "I feel Irish. I don't think you can take Belfast out of the boy." He also attributes his "love of words" to his Irish heritage.

To contrast, Fowler also grew up in Ireland during a very tumultuous time. He also had to "reject" his Irish identity at some point, instead identifying himself as British. But, unlike Branagh, he entirely rejected it. Instead, he identified with and took on the characteristics of the English. He become the oppressor rather than the oppressed.

I don't have a fully formed idea of this connection yet but I remember when I learned Branagh played Fowler and I already knew that about Branagh's upbringing I really was fascinated that they chose him.