Reducing the problem to ‘people coming from overseas’ is an equally reductionist argument.

There are properties going unused, for very many reasons. Second homes, holiday homes, etc. This also drives the price of properties up. This is one of the inputs to the problem. Planning permission laws is another input. The size and change of size of the people needing housing is another input.

Is it not the dominant factor, at least in the short term? It's much faster for 150k people to enter/leave the UK than for a corresponding number of homes to built/demolished.

It does, but occupancy rates in the UK are already incredibly high compared to countries like France.

There are simply too many people and not enough houses.

reductionist in this case is not a bad thing. We need a major change to fix this situation and doing some little tweaks like increasing taxes on second homes or holiday homes does not actually fix this (we already tax those specific cases, with things like second home stamp duty or in some areas second home council tax).

You have

A - Demand (immigration of 1 Million per year)

Or

B - Supply (building only 120,000 houses per year)

We MUST fix one or both of these sides of the equation. Holiday homes aren't going to add up to a row of beans quite frankly (and will have very negative effects on the tourism industry, not so bad in London - but might be quite an impact in cornwall for example).