Question: Which 1961 British comedy film directed by Edward Buzzell takes its title from an English language nursery rhyme of nineteenth-century American origin?

Context articles: As I was going by Charing Cross
One, Two, Buckle My Shoe
Three Little Kittens
Row, Row, Row Your Boat
One, Two, Three, Four, Five
Mary Had a Little...
Mary Had a Little Lamb
A Wise Old Owl
There was an Old Woman Who Lived in a Shoe
See Saw Margery Daw

"As I was going by Charing Cross" (sometimes referred to as "As I was going to Charing Cross"), is an English language nursery rhyme.
 The rhyme was first recorded in the 1840s, but it may have older origins in street cries and verse of the seventeenth century.
 It refers to the equestrian statue of King Charles I in Charing Cross, London, and may allude to his death or be a puritan satire on royalist reactions to his execution.
 It was not recorded in its modern form until the mid-nineteenth century.
 It has a Roud Folk Song Index number of 20564.
"One, Two, Buckle My Shoe" is a popular English language nursery rhyme and counting-out rhyme.
 It has a Roud Folk Song Index number of 11284.
"Three Little Kittens" is an English language nursery rhyme, probably with roots in the British folk tradition.
 The rhyme as published today however is a sophisticated piece usually attributed to American poet Eliza Lee Cabot Follen (1787–1860).
 With the passage of time, the poem has been absorbed into the "Mother Goose" collection.
 The rhyme tells of three kittens who first lose, then find and soil, their mittens.
 When all is finally set to rights, the kittens receive their mother's approval and some pie.
 It has a Roud Folk Song Index number of 16150.
"Row, Row, Row Your Boat" is an English language nursery rhyme and a popular children's song.
 It can also be an "action" nursery rhyme, whose singers sit opposite one another and "row" forwards and backwards with joined hands.
 It has a Roud Folk Song Index number of 19236.
"One, two, three, four, five" is a popular English language nursery rhyme and counting-out rhyme.
 It has a Roud Folk Song Index number of 13530.
Mary Had a Little… is a 1961 British comedy film directed by Edward Buzzell and starring Agnès Laurent, Hazel Court and Jack Watling.
 It takes its title from the nursery rhyme "Mary Had a Little Lamb" and is about a slick impresario who tries unsuccessfully to win a bet with a psychiatrist over the production of a perfect baby via hypnotism.
"Mary Had a Little Lamb" is an English language nursery rhyme of nineteenth-century American origin.
 It has a Roud Folk Song Index number of 7622.
"A Wise Old Owl" is an English language nursery rhyme.
 It has a Roud Folk Song Index number of 7734 and in The Oxford Dictionary of Nursery Rhymes, 2nd Ed.
 of 1997, as number 394.
 The rhyme is an improvement of a traditional nursery rhyme "There was an owl lived in an oak, wisky, wasky, weedle."
"There was an Old Woman Who Lived in a Shoe" is a popular English language nursery rhyme, with a Roud Folk Song Index number of 19132.
 Debates over its meaning and origin have largely centered on attempts to match the old woman with historical female figures who have had large families, although King George II (1683–1760) has also been proposed as the rhyme's subject.
"See Saw Margery Daw" is a popular English language nursery rhyme, folksong and playground singing game.
 The rhyme first appeared in its modern form in "Mother Goose's Melody", published in London in around 1765.
 It has a Roud Folk Song Index number of 13028.