I think you're still working class but your children would be more likely to be middle class. Or at least, that's how I always thought it worked. Possibly the working class might sneer at you with your fancy ways and degree, the middle class might accept you as an honorary member as your children find themselves enjoying a more middle class lifestyle than you did. It seems to be much simpler in America where it's all about the money, and nobody cares who your father was, you make your own destiny. Personally I tend towards the British view that you are a product of your upbringing, and there is nothing you can do to change it.

And then there the whole aristocracy versus meritocracy. Just because you're smart and work hard and succeed doesn't make you posh, and goodness knows there are some monumentally stupid people in the upper classes.