Oh, where to start with this.
1. Immigration is a scapegoat for a significant lack of investment over the years. The Government of recent years made the mistake of assuming everything the Government spent money had a net loss for the Treasury (ignoring proper costs analysis or the medium to long-term effects of investment). A lot of the areas they've cut over the years are actually of benefit to the treasury in the medium to long-term in terms of increased tax revenue.
When you don't invest properly in local businesses, hospitals, schools, social care etc. you effectively bleed the councils dry before they've even had a chance to allocate the funding. Instead of blaming our politicians for their incompetence we seem to be blaming immigrants which effectively gives their incompetence a free pass.
Also, migrants don't get pushed to the front of the queue. Not even EU migrants get pushed to the front as they have specific eligibility criteria they need to meet, same as the locals. Now, either the migrants getting these benefits are a lot worse off than you think or you need to complain about the way the Government setup the eligibility criteria. Non-EU migrants are in an even worse as they have even stricter criteria to meet.
2. What you described is most likely a refugee situation, and in those cases the families don't have the right to work and therefore can't rather than won't. Also, the family you describe are incredibly poor compared to the vast majority of people in the Country which contradicts your point about most poor being local Brits. Even then, its not exactly difficult to imagine most of the poor being local Brits considering they make up most of the UK population.
Furthermore, if we look at actual economic migrants, they pay more in taxes than they take out in benefits, NHS, school and social care costs. The data is all there and flies in the face of the rhetoric in the papers.
Currently in the UK we have some of the most incompetent and shameful politicians for generations (across the whole political spectrum), but people still just want to blame it on immigrants and let the politicians shit all over us.
I dont know about the rest of your post since i dont live in the uk but i have family who live there and i go visit. But ill tell you here in ireland the bolded is very much true and a number of my family members have said its the same in the UK. Hell over here in Ireland if your a refugee your pretty much giving a house as soon as you come well our own are left with such a hard time to get a house.
England done the right thing leaving the EU and i hope Ireland will do the same thing and fuck the euro give us back our punt!!.