I've been reading "Speaking for Themselves", being the personal letters of Winston and Clementine Churchill, and came across this characteristic exchange:
Winston to Clemmie, 25 June 1911: ""At luncheon Barrie arrived - but I am v[er]y sorry to say that he went off again unexpectedly this afternoon without my ever having a talk with him. I am vexed at this because I am sure I like him - and always something crops up to prevent my getting to know him."
Clemmie replied the following day: ""As soon as I come back we will entice Barrie to luncheon or dinner but he is dreadfully shy & has to be much coaxed. We must have him alone or with only one other choice person as he is always silent when invited to perform."
Clemmie knew the Llewelyn Davies family as they were near neighbours in Berkhamsted, and came to know Barrie on his frequent visits to Egerton House. Churchill subsequently met Barrie several times. In 1924 he proposed a toast to "Sir James Barrie, Literature and the Press" at the Printers' Pension Corporation dinner, and in 1932 was among the guests at a lunch-party in Barrie's Adelphi flat, given to celebrate Lord (formerly Sir Edward) Grey's 70th birthday. Nico remembered meeting Churchill at the flat in the early 30s - "unsurprisingly, he and Uncle Jim got on like a house on fire!" Although to my knowledge no photograph exists of the two men together, there is one of Churchill and Peter Pan - taken in 1958 when his daughter Sarah played Peter.