The BFI's Screenonline website relates how Mackendrick scripted and storyboarded five of George Pal's Horlicks commercials in the thirties, before coming to work for John Halas and Joy Batchelor at the animation department of JWT Productions early in World War II. Denis Gifford's filmography credits him as writer on Train Trouble (1940), a Kellogg's Cornflakes advert; The Pocket Cartoon (1941), a political satire; Carnival in the Clothes Cupboard (1941) and The Fable of the Fabrics (1942), both soap adverts; and the Abu series, a set of propaganda films for Middle Eastern audiences. He also worked as a designer on at least some of these films.
In 1942 Mackendrick and MacDougall started their own production company, where they made the short propaganda films Save Your Bacon (1942), Contraries (1943) and something called Nero or Fiddling Fuel (1943) which is not listed by Gifford and may have been live action. Save Your Bacon is available for viewing and purchase at the British Pathé website; consisting mainly of still pictures with minimal animation, it encourages viewers to save household scraps so they can be used as feed for pigs. The title sequence contains a spot of live action puppetry.
I have not seen Contraries, but Gifford provides a synopsis:
Propaganda cartoon for the Ministry of Supply. Inspired by the poem "The Walrus and the Carpenter," these two characters collect waste paper and point the moral, "sort your salvage." Item in Pathé Gazette; released 1 July 1943According to the BFI database, Mackendrick later served as a consultant on Halas & Batchelor's Handling Ships (1945) and the Charley series. MacDougal, meanwhile, went on to script the Larkins shorts T for Teacher (1947) and Men of Merit (1948).