I found some enjoyable articles while I was trying to find out the name of Bertie's equerry in the movie (Harold Campbell -- I knew it wasn't James Stuart, who introduced Bertie to Elizabeth and was later sent packing by Queen Mary because he was courting Elizabeth himself), and I figured I should share them!
Here is an article with the tabloid headline "Revealed for the first time - the other woman in the Queen Mother's marriage" though there is no suggestion that anything went on between the prince and the woman, whom Elizabeth tried to have made a Dame long after Bertie's death: "Evelyn Laye, seeing how much Bertie dreaded public speaking, recommended to his private secretary, Patrick Hodgson, the services of the London-based Australian speech therapist, Lionel Logue. Later, in the utmost secrecy, Laye herself took a hand in trying to cure the Duke of York's stammer. She would invite him, incognito, to a West End rehearsal studio where she would give him deep breathing exercises, after which they would both sing his favourite Evelyn Laye songs."
Here is a long lovely excerpt from William Shawcross's The Queen Mother: The Official Biography about Bertie and Elizabeth's courtship: "In July 1920, a few nights after being formally presented at court, Elizabeth Angela Marguerite Bowes Lyon attended the Royal Air Force ball at the Ritz. Prince Albert, King George V’s second son, was also in attendance with his new equerry James Stuart. Many years later, Stuart wrote in his memoirs that Prince Albert had asked him that evening 'who was the girl with whom I had just been dancing. I told him that her name was Lady Elizabeth Bowes Lyon and he asked me if I would introduce him, which I did.'"
And here is a respectable news article, "Oscar-tipped movie The King's Speech ignored George VI's key mentor" about the other man in Bertie's marriage, hahaha: "It was Sir Louis to whom the then Duke of York confided the most intimate details of their honeymoon. 'Everything was plain sailing, which was a relief. You know what I mean. I was very good!', the jubilant Prince wrote to his older friend."