There are alot of manual jobs that tend to be filled by migrant workers that the unemployed or plain lazy should/could be doing... trouble is those people see things like cleaning as being beneath them
better to be working than scrounging, if only for the sake of pride surely 
As already suggested, the majority of those who have come here from Poland and the like have a solid work ethic and have come here to work, so will gladly do the jobs that many here wouldn't inspite of some employers paying them less than they might pay locally. And I very much doubt that they choose to come here for the hell of it... I mean, would you leave the UK and move a couple of thousand miles away from your family/friends to a country whose language is not your own unless there was a significant improvement in your life?
Didn't think so...
Nail on the head comes to mind

To that, you can add the immigrants that have come over here legally, got there head down and kept there mouths shut, learnt a trade and got on with making a life for themselves and there family instead of whining and whinging about pay, pensions and conditions all the time.
It has got to the point where if the UK firms have the choice of 2 potential employees with identical qualifications ....... 1 British and 1 foreign then they will pick the foreign person because they have a better chance of a decent days work out them

Its becoming a common pre conception that all UK workers are lazy barstewards

Well that 'dangle berries' too

There are a hell of a lot of people out there who WANT to work but are never given the chance because they are deemed too old, or get tarred with the same brush as the wasters who hang around the jobcentre every 2 weeks
In my part of the world, the unemployment is that bad that by the age of 40, you are on the scrap heap unless you can get one of the very few skilled jobs around through the back door / contacts inside the firm so to speak.
The manual labour jobs are mostly zero hour contracts / temps now and you have no choice but to go through a agency.
The biggest problem in that is that most of these agencies may be UK registered companies but they are only interested in employing non UK workers because of the stigma that surrounds us.
As for the petition, waste of time for the reasons already said BUT signed because it made me feel a little better for 5 minutes

Solution to the problem ..................
Tell the EU to stick it
Close the borders for 5 years minimum to unskilled workers whether they have a job waiting though one of the dodgy agencies or not.
Start a phased deportation of non skilled workers and replace them with British born workers.
If the British worker does not pull his weight then he get no welfare whatsoever and starves

Make a list of the skills this country needs to survive. These courses should be massively subsidised by the British tax payer for the benefit of the students BORN in these islands. Not somebody who arrived here under a lorry because some garlic crunching security guard in Calais looked the other way with his governments blessing, hung around the social security office for 10 years bleating asylum then get handed a passport by our wonderful government of the day and being told they are now BRITISH
Some of the money saved from leaving the EU should be ploughed back into full time education to pay for this and infrastructure projects in the areas of the UK that needs it, NOT Kent and the south east / west who have had the lions share of money for too long

Bring back National Service / Work parties for those lazy scumbags who refuse to work for a living.
I'm sure out outposts like the Falklands could do with some forced labour to do manual work and improve there infrastructure (roads ect)
Also tax breaks for all companies who employ British workers so it makes it more economically viable.