Here's an article which says that public transport byelaws meant that carriages had to have enough room for hats.

(http://www.inlondonguide.co.uk/who-are-londoners/bowler-hat-...)

> Taxi design at the time (horse-drawn cabs - Hackneys) stated the height of the cabin had to accommodate a man wearing a bowler hat and like many of those bye-laws, they remain in place today.