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).