This is a little curio. In the 1944 Tommy Handley film Time Flies, Handley and a couple of New York entertainers played by the wonderful Evelyn Dall and George Moon get zapped back to the Elizabethan era in a time machine that surely inspired the Tardis nineteen years later. I'd love to show you the time-travel scene (where our travellers collapse, incapacitated, as it takes off) but unfortunately I no longer have the technical means to do so. I can however bring you the two superb scenes where Evelyn Dall's character helps Shakespeare write Romeo and Juliet, and then (it being a musical comedy) she and the George Moon character burst into song to throw their pursuers off the scent, Shakespeare looking on approvingly, and the lead violinist being the young Stéphane Grappelli. I think this will cheer you up. (There's no Tommy Handley in this extract, which is frankly a bonus.)
Shakespeare here is played by John Salew, who also has small parts in Kind Hearts and Coronets and The Lavender Hill Mob.