I've met that type a couple of times
A sloaney young student in large designer sunglasses (in winter of course) once did the exact same thing to me. Perhaps she's the daughter of your arrogant posh middle-aged lady.

Another time, I was on a bus when a middle-aged lady came on, dragging her toddler son with her. He threw himself onto the floor and had a tantrum as toddlers do, blocking the door for other passengers. She didn't try to move him out of their way (although she's had no problems moving him earler), just hit him and swore at him, which only seemed to make his tantrum worse.
An old lady who wanted to get off the bus said, "I'd like to get off please, perhaps you could try moving him instead of hitting him."
The middle-aged lady went crazy and started shouting, "Don't you know I'm a respectable middle-class person, how dare you tell me how to raise my children, nobody can tell me what to do (etc etc)" in a very obviously-put-on posh voice that she hadn't had before, before pushing the old lady off the bus.
(MC Toffeehammer, Sat 26 Jan 2013, 21:26, Reply)