It's pretty cool that ol' Winston Churchill shows up now and then in this movie… since he would go on to be British Prime Minister and one of the most important figures in modern history. (No big deal, right? Wrong.)
As many historians (and screenwriter David Seidler) could tell you, Winston had a good sense of humor, which makes him ideal company for Elizabeth Bowes-Lyon. When Elizabeth asks him if she was too rude to Wallis Simpson, Winston takes her side in saying dryly,
CHURCHILL: On the contrary, your Royal Highness. Etiquette decrees royalty must be greeted by the official host: in this case: the King. Not a commoner. You behaved impeccably. As always.
Despite his humor though, Churchill is a serious dude with serious concerns about Britain. For starters, he tells Bertie that,
CHURCHILL: There were those that worried where [David] would stand when war with Germany comes.
In other words, Churchill knows that England will need a king that it can rally around for war, and Churchill knows that Bertie can be that king. To help reassure Bertie, Churchill even reveals an intimate part of himself, admitting that he once has a speech impediment too. As he tells Bertie,
CHURCHILL: Family secret. Tongue-tied. An operation was considered too dangerous. I eventually made an asset of it.
So even in weakness, Churchill can find strength. And it's no doubt this kind of attitude that made him such a successful man.