Not sure I agree with this. My parents firmly WC, dad in particular 1st gen immigrant and grew up pretty poor.
However, by the time I was born (the eldest of 3) we lived in a 4 bed detached house with a huge garden in the posh part of town in the SE.
We never went on package holidays, went to museums, ate round the dinner table, was an expectation that we would all go to uni.
My dad worked in insurance, had a secretary, led a team etc my mum was part time around childcare. We had two cars, able to go on school trips etc
I'm struggling to see how I wasnt a middle class child? My children recieve all of the above and more as myself and DH are both full time in professional jobs, so they are firmly middle class.
I'm not being defensive, it honestly doesnt matter! But I do find the concept of not being able to move class interesting.
Despite being poor and WC I would say my das grew up with quite a bit of social capital - a perk of being born in London I guess!