This looks like conjecture to me. I'd like to see some statistics on the immigrant 'burden' on social housings.
And why would immigrants come here to go on a social housing list? The absolute majority come over to find work or have to get a job or find themselves staying and end up working. We criticise them for taking 'our' benefits yet they are also criticised for taking 'our' jobs.
Which is it?
You do realise many people have jobs and live in council houses?

Where did I say the immigrants don't work? I say they do... in the main low skill labour which should be filled by natives who are currently out of work... but especially the long term unemployed.