If you tax the rich more, they just compensate by cutting wages which makes poor people poorer.
If you increase the minimum wage, the rich cuts jobs to compensate.
Also, higher tax on the wealthy causes multi-national businesses to either leave or setup abroad which moves British jobs abroad.
The harsh reality of Socialism: Doesn't work. Eventually you will run out of other people's money.
Harsh reality of capitalism: Born into a low-income family? Have fun cleaning toilets for a living. University, they won't even take souls for payment, so nope. Basic education (pre-university): Poor. And it may be parents' own mess they got themselves in, but what are the children supposed to do?
Harsh reality of socialism: If you tax the rich more, you get more money. Depending on how much you tax and how much these rich want to spend, they still want good quality so they won't decrease the minimum wage (in general). Minimum wage is a ridiculous idea which Belarus has practically done away with, if you don't want to work for a low pay, you're free not to. We need higher taxes all around the stable world, EU is a good organisation for this.
Go visit the Nordic countries, have you ever visited Estonia? It's wired.