There is certainly such a divide. Women in the north of England and Scotland are often shorter, hardier and more inclined to make a statement with their appearance and demeanour (not always attractively). Altogether, those factors tend to promote high heels - and bare legs/sandals/no coat, even in cold weather.
From my own observations, men in the north tend to dress in a much more casual and often sloppy manner - unless at a formal event, such as a wedding, when the waistcoats and ties - albeit typically left undone as soon as possible (ugh!) - will be seen. I suspect that this male contrast and discomfort stems from a working-class background: a miner or shipwright for example would tend to dress in rather shabby clothes but have a 'Sunday best' suit in which he was never really comfortable - and which was often in the pawnshop when not immediately needed.