It's funny that it's women arguing about the dress codes in offices.
In the vast majority of offices that actually have strict dress codes in London (ie legal firms etc) the code is "Men wear full suit, with Blazer at all times and all seasons, no matter how hot. Women wear whatever you want as long as it looks smart and professional".
Granted there's debate on whether heels automatically make a woman look more professional or not but codes tend to be much more lenient in their favour.