Logically, if there is a reduction in immigration to a country or area when compared with historical averages, or alot of people currently residing in one country or area; leave, the need for housing will reduce; as by sheer numbers wise there are now less people in the area or less people coming to the area, and because of that change, there can theoretically be an over supply of housing with less people to occupy it, prices can come down to entice people to those properties if the change in population has an affect, so whoever said that isn't wrong strictly speaking, but even I can see that something like that wouldn't happen overnight, and would be an ever so miniscule change over a long period of time, £1 million houses in London aren't suddenly going to drop to £200k because Vlad and his pals have went back to Poland. But something to remember, reduction in immigration and end of free movemenet was never guaranteed anyways but I still voted leave.
And for what it's worth, anyone can rent a bus and vinyl wrap slogans onto the side of it, doesn't make them true or binding, especially when coming from a personal interest group, which what both leave and remain were.