While we may never see James MacAvoy or Patrick Stewart on Legion, the show finds creative ways to play in the X-Men universe in subtle ways. Was David's British accent on Legion a reference to Professor X? His "rational mind" sounded a lot like Charles Xavier, David Haller's birth father in Marvel comics. This could be a clue.
Trapped by the parasite in a kind of mental coffin, David was able to have a conversation with himself and start putting the pieces together. He rationed that his father was a powerful mutant, probably a psychic, who fought the monster (Amahl Farouk, the Shadow King in Marvel comics) in the astral plane. In the comics, Xavier defeated Farouk in a duel just similar to what David speculated on Legion. The illustrations on the chalk board also looked like comic book panels, which I thought was a charming touch. David then speculated that his father hid him away as a baby, but Farouk found him and has been poisoning his mind ever since. Did you notice that the drawings of David's father didn't include hair, either?
When David spoke as his father in an exaggerated voice and Rational David quipped "is that your British accent" — I think that was the biggest clue. It's a semantic slip that gives away the fact that David's father is English.
On the other hand, this dramatic device could have been just a chance for Dan Stevens to relax, use his natural accent, and poke fun at how Americans are intimidated by the British. We assume that anyone with an accent from across the pond must be smarter than us. Either way, it was a fun way for David to have a rational conversation with himself and learn more about where he came from on Legion.