Which of the following way of writing date is more common or recommended for using in British English in official and formal documents, and why?
Or they are both the same and it's a matter of style?
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The formats both mean the same thing (either April 9 or September 4). Stating numbers without leading zeroes is the standard when mentioning a date in isolation or as part of a sentence, e.g. "The tournament will start accepting entries on 4/9/2018."
Normally you would use leading zeroes in your date format when you have a column of dates and you want your column to look good and be more readable; having the date parts aligned vertically is much more visually pleasing than letting them jump around. Consider:
the ugly way:
prettier, easier to read: