The majority of the immigrants are not exactly in a position to buy houses, they might cause some rent inflation but you can't categorically tie immigration to house price inflation like that.

The better explanation is that real estate is just about the only thing that can boundlessly go up in price without any perceived increase in quality or performance and so it tends to be a sink for surplus wealth generated by a nation. On top of that there are a lot of wealthy people competing with each other for investing in the UK real estate market (and those are not just UK residents) and interest rates are at an historic low which tends to drive up prices.