On the subject of migrants, this document makes interesting reading:
EU migrants: entitlement to housing assistance (England) - Commons Library Standard Note - UK Parliament
If you don't want to read it all I have copied some relevant paragraphs below, and page 11 onwards deals with the question of whether migrants jump the queue.
There is no general entitlement to social housing
for anyone in England, including British citizens. [Emphasis mine] It should also be noted that even those people from abroad who may be eligible for housing assistance still have to qualify for assistance in line with an authority’s housing allocation scheme, or meet the criteria under which a statutory duty arises to households that are homeless (Part 7 of the 1996 Housing Act (as amended)).
Allocation of social housing
Foreign nationals are eligible for an allocation of social housing if:
in the case of European economic area nationals, they have a relevant right to reside, for example, if they are working, self-sufficient, or have a permanent right of residence in the UK (after five years lawful residence in the UK),
in the case of other foreign nationals, they have been granted leave to enter or remain in the UK with recourse to public funds (for example, people granted refugee status or humanitarian protection).
Where foreign nationals are eligible, they would have their housing needs considered on the same basis as other applicants in accordance with the local authority's allocation scheme.