Workers are not unwilling to work. Rather, they are smart enough to realise when they are being fucked over for less than nothing nothing and are unwilling to work for a poverty wage. As has been said, immigrants will work for less than indigenous workers because either a) their situation is far worse than working-class people in Britain for a variety of reasons and they will do anything to ameliorate the bad conditions even slightly or b) they have the option of saving their money and moving back to their home country where it is worth far more.
I've worked with immigrants from Eastern Europe, one was a Pole, his fiancee and him, both teachers, had come to Britain to work because they were earning more money in Britain. He worked as a labourer, she worked as a food stand attendent. They earnt more doing those jobs than they did as teachers in Poland. They've since returned to Poland having saved enough money to allow them to start a family and live decently. British workers do not have that option, they are stuck in Britain on poverty wages in poverty conditions for the rest of their lives.
Yes, having some meagre benefits means that some people will rather not work shit wages and live on benefits instead, but this is a tiny minority out of the working-class in this country. Most people who don't work have valid reasons or circumstances which prevent them working. Either mentally/physically disabled people who simply are incapable of the work offered to them, young people failed by the education system who cannot find decent work with the poor marks they have achieved, or single mothers who can't afford decent child-care on the meagre salary that is offered them. Without free child-care single mothers cannot work on the minimum wage cause the cost of private child care leaves them worse off than if they stayed on benefits! Thats far more a cause of people not working than this supposed non-existant "can work/won't work" attitude.
I don't blame workers for not wanting to take poverty wages. I do however think that everyone should work, but that this work should be productive, socially necessary and on a living wage, not the poverty/minimum wage. I'm not in favour of refusal to work, I'm in favour of workers and the unemployed fighting for well paid, productive and socially necessary work for everyone. The working-class taking control of society, getting rid of parasitic and unnecessary jobs and dividing the rest of the working-week up amongst society as a whole would cut hours and give people the productive work they need as human beings while giving them the free time they needed to forge proper social relations, grow and develop and not be alienated. Obviously society would need to be under the control of the workers to do all this, but thats why I believe in the necessity of revolution.
Those things would solve poverty and the supposed "problem" of people with a "won't work" attitude.