It is widely known that an Englishman would carry an umbrella by holding it in the middle and having the pointy end point forward
This is correct. The reason is obvious; you always know where the pointy end is, and it remains under close control. No Markov "accidents" possible this way!
but it's also used to carry an umbrella 'as a walking-stick' -how exactly does that work?
Umbrellas aren't really designed to be used as walking sticks if they're the more typical two-piece "fit-up" style. They tend to end up bending under body weight or the thin point catches a gutter or groove. You really need a solid-stick brolly for that; they're sturdier and have wider/blunter point. I often use my brolly in a similar fashion to you so got a solid-stick as my dressy black brolly. My casual navy one is a fit-up though, and I must admit to abusing it by using it the same way.
If you use a brolly as a stick, the strictest person would say that you should use it the way you would a cane, for support when needed, and not otherwise.
However, personally, I tend to adopt the same rather more louche habits around a brolly as you do!
One other thing a brolly is good for - even if it's a bit peremptory - is for subtly guiding pedestrian traffic when there's that momentary "you first, no you, oh I insist" type of shuffle. It makes it obvious which direction you're moving in.