It's a little back of the envelope because it's so many factors, but...
On the demand side, over the last 40 years, net migration has been approx half of population growth. Natural changes (longer lives/births) have been the other half.
The reduction in average household size, is the other big factor on the demand side. It's dropped from around 2.7 in the late 70s to 2.2 in 22/23, which would be equivalent to an 12 million increase in the UK population. It's actually increased due to the natural changes, and net migration, by around the same figure million, so it's a bigger factor than either of those two.
That brings us down to maybe a 20-30% of the demand side being down to migration.
If you look at the changes in house building, and in particular, social housing, which tailed off from the late 70s. Then there are plenty of other supply side issues, such as the rise in second homes, investment properties, holiday homes etc., then overall that reduces it further.
As I said, it's probably a research project to get it anywhere like bang on, but that at least gives you an idea.