So its not immigration causing this, like we've been told time and time again by those of a right leaning preference?
It's not so much immigration, rather the freedom to work for some people who come (came?) to the UK to earn more than they could at home. People who only intend to stay a few months or a year or so aren't worried about mortgages and financial stability for the future, and are likely happy to rent (as is common near me, including my next door neighbours) and share rooms with others doing the same. A 3 bed house could house 10 or more people, and in some cases the bedroom is used by different people (shift workers) so each has the room for 12 hours only.
They can do this because they send the money home and a small amount of pain is worth the gain. We talk about British people being too lazy to take these jobs, but it's probably fair to say that you won't have much of a life if you were to take them. Fine perhaps if you lived with your parents and had no aspiration to leave.
Employers have been exploiting this cheap labour and may have a nasty shock if and when people go home, as is already happening now eastern Europeans are getting less money after converting to Euros or their local currency, and left wondering why they're in a country that seemingly hates them, when they could do similar work for better money in places like Spain that are more welcoming.
The far right does of course seem to want to lump those who are here, quite legally, doing jobs we don't want to do (for whatever reason) with the illegal immigrants and other foreigners, the latter of which leaving Brexit has nothing to do with.
Ironically, the jobs that can't easily be automated, such as cyclist working for Deliveroo and having to risk life and limb to bring food on time to the door, will likely be the jobs we are left with. Who will do this work?