Assuming that people less well of than oneself are lazy and not making an effort is part of the class system!
I agree, and also think that the lack of social mobility we keep hearing about only really affects the upper working/lower middle classes. These are the people who benefited from things like free education in the 60s and 70s.
Poorer people had to think about contributing to the family via 'board' money, and this was enough to stop a lot of families from encouraging their children (particularly daughters) from going to university. It was the families of skilled workers and lower admin workers who were able to educate their children because of grants and an expansion in places. They now expect their own children to automatically go to university, and to continue the family's trajectory, yet the very expansion that benefited them has decreased the scarcity value of degrees, and thus the elite status that they used to provide.
Meanwhile, families who for generations have been in the professions will continue to be ok - they just swap school fees for university ones, and buy their kids a car with the difference. It's less that fortunes of the former group have reversed, than that there was a temporary window during which they got a better deal.
Also, there are fewer jobs in factories, mines and so on, so those who would once have taken them are now working in call centres, retail and hospitality - the precariat - but because this is not traditionally manual work, they often define as middle class, even though they do not have the same protections and life choices as the more established middle class.
In reality, it is these protections and choices which define middle class status. Paid sick leave, decent pensions, professional body protection, insurances and the ability to save for a 'rainy day' make all the difference when it comes to social mobility, as does an understanding of what is available when it comes to making career choices and decisions.
Assuming that it is a lack of ambition that stops people from being more mobile is far too simplistic, and yes, a classic side-effect of a class system that is justified by a false assumption that we live in a meritocracy. It's one thing to retrain when your sector is floundering if your parents can give you a leg up, and quite another if you have to keep supporting yourself and your family throughout. It's much easier to get onto the housing ladder if your parents have made a lot of money on a house (usually because of the postcode lottery that has existed since the 70s) than if they also rent and have no spare cash, and so on. To then claim that you have managed by hard work is very unfair, if not disingenuous.