I don't think creating an 'underclass' enables the middle classes to remove themselves from the 'working class'.
A friend and I were discussing recently how his mum lived in a 'working class' area and had as much pride in her conduct and appearance as her neighbours did. She scrubbed her front step daily apparently!
The 'working classes' have traditionally and historically worked hard, done their best by their families, aspired to 'better' themselves either educationally or financially.
There are some skewed ideas of middle class nowadays. It's an unhelpful term because for some people it means money, others education, others manners and conduct. For my mum, being middle class means owning your own home (outright not mortgaged because that describes her) and not living hand to mouth (i.e. being able to save rather than relying on 'the never never'). For me, it's about conduct, education and occupation. For some of my neighbours it's about how stylish and 'classy' your home is and where you do your shopping (food and clothes).
The 'underclass' for me describes the 'entitled' the "I know my rights". Those who are happy and willing to play out their whole lives in public either on the streets, on FB, on JK. Those who don't have respect for themselves, others, where their live, society/community. Those who have removed themselves from 'respectable' society. Those who are brazen about their lack of education/employment and wear it as a badge of honour (and yes, I have met/known those people). For me, a lot of 'class' is about attitude rather than tangible things like wealth. And yes, I think that some very wealthy people are members of the 'underclass' - they just have the means to keep themselves out of it on appearances.
There is nothing not respectable about working - whatever your job is, how ever much money you earn or whoever owns your house.
There are people who say that the welfare system is partly responsible and I agree. Anyone who has ever claimed benefits for any length of time, or lived in areas where there are a lot of people who do, will know that it is perfectly possible to present yourself/be middle class and live on benefits. It is also perfectly possible to be a member of the 'underclass'.
I was a single mother on benefits living in social housing when my son was young. And no one knew (who didn't actually know of course!). I had the same standards, values, 'lifestyle', conduct and attitude towards myself, my family and society (good and less good!) when my income was benefits as I did when I was a married professional graduate and we had a combined household income of £50k.
Phew that was long!