The idea that immigrants and asylum seekers get preferential housing from the government is a complete fallacy. I'd like to see you present some facts and figures on this, as opposed to "a story".
Firstly, just being a regular immigrant entitles you to nothing. You have to rent privately or get a mortgage like everyone else.
If you are an illegal immigrant, you are entitled to absolutely nothing. No benefits, no housing, nothing, because you're illegal.
If you are an asylum seeker you are entitled (as agreed by the UK under a UN Charter) to having a roof over your head. This could be a detention centre, a hostel or a basic B&B.
If you are get accepted as a refugee - you will get housing for a finite period - again this could well be a hostel or B&B. In London, it is nearly never a house.
The problem is, that many councils sold off their council housing in order to generate money, and now have very little of it left.