Pointing out how poor our minimum wage is (contrary to popular opinion) isn't justification to cut welfare for those who also live in poverty.
I think you will find most people who are in favour of us having a reasonable welfare state to look after the poorest are ALSO in favour of increasing the share of earning for the lowest paid in society.
I agree that people who work a full week deserve to be able to live a life, just that to pay for that we should not thrust those living on the line further into poverty.
Say we slash the benefits of the bottom 10% by a set percentage, this will have a social & economic impact.
Crime rates will increase
Mental illness will increase
Poor health will increase
More of the very behaviour you want to prevent will continue to expand & will do so at a faster rate.
Making life harder for people doesn't make people suddenly able to change - if that was true nobody would be starving in Africa - great adversity actually tends to have a detrimental effect of people, reducing their ability to handle stress & get out of the band situation.
What many are proposing is to use the stick, when all of our understanding of human behaviour & our social sciences say we need to use the carrot.
But hey, let's not let little things like facts & science get in the way of your ideology.
		
		
	 
At no point have I said that I believe state benefits are intrinsically a bad thing, which is what your response suggests, I would much prefer to live somewhere that takes care of its citizens.
What I have said is that, I have irrefutable evidence that it is currently possible for multiple generations of immediate families to live purely off state benefits in a way that the current minimum wage does not allow, in fact it can allow a level of lifestyle that some could only dream of. It can (relatively easily) offer a next to free roof over your head that is maintained for you, enough sustenance to make you and those you care for fat and enough spare cash to allow it to be frittered away on having a million and one channels through Sky (because Freeview just isn't good enough), having money to hand over at your local pub very regularly and then to head to get take-away afterwards, or to go down to your local supermarket and buy a bottle of liquor of your choosing. 
State benefits should NOT allow for at least some of these things (I am undecided about the roof as it's a thorny issue) but currently I have proof that it does. This is wrong.
EDIT: I forgot to add the crucial point, all of this (admittedly meagre) luxury is possible for somebody who DOESN'T WORK. They don't get up at 5 in the morning and work their lives away 12 hours at a time or even just get up at 9am and go to an office for 8 hours. They do nothing, their life is theirs to lead as they wish. They get up when they want, do what they want (bar the odd meeting with some form of council worker). This lifestyle should lead to nothing but a basic form of existence, otherwise where is the incentive for those without a sense of basic morals and self-worth to join those working for the same, or even lesser, lifestyle?
Also, I am intrigued, at the moment we use the carrot approach, somebody who isn't working for minimum wage can have a better lifestyle than somebody who is, if this is not the carrot approach then I don't know what is. So with this in mind, what is the carrot approach you speak of that we should be using to make working and becoming a generally responsible human being who takes their own future into their own hands an attractive prospect? 
With this in mind, should we also cease to punish children when they do wrong by sending them to their room or by removing an unnecessary luxury and instead congratulate their ingenuity for being able to draw on the walls or punch their sibling or whatever it is they have done and if so, how do we go about this pat on the back? 
Honestly I am interested to hear your actual plans to implement this rhetoric based loosely in scientific findings?