Android - How to change date and time format on Marshmallow?

In Android Marshmallow you don't seem to be able to change the date format. Instead it chooses automatically what's appropriate for your locale.

In your case, you seem to want the English (UK) variant and not the English (US) one. So go to language settings and change it. Any other English variant should work since I'm pretty sure only americans use the MM/DD/YYYY variant.