Net migration (immigrants - emigrants) in 2024 was about 0.63%.
I would hope the productivity advances in the last 75(!) years would allow the Uk to build enough homes for 0.63% growth, when our 1950s tools and technology allowed them to accommodate a 0.52% growth
In the past, the population was growing even while net migration was negative. This means people were having babies. This trend reversed in the '80s and migration has made up somewhere between 37% and 128% of annual population growth since then.[1]
There'd have to be some incredible innovation to overcome increased regulation around zoning and dwelling construction generally, NIMBYism, financialization of everything, and a preference shift towards living in land-scarce cities (urban population up ~145% since 1950).
1: https://www.worldometers.info/world-population/uk-population...
Meanwhile the baby is essentially a net drain on productivity, whereas an immigrant is not.
To your point about phase-shifting though, I think that's a definite possibility, but relies on preferences of each community, and how they change by generation.
Urbanization is not solely driven by immigrants, but how likely are immigrants to move into lower density housing when they have kids? What about their kids? And their kids, etc? And compare that to non-immigrant (or non-recently immigrated) preferences.
The relative productivity of babies and immigrants is not of interest to me in talking about housing preference, but you're correct that babies don't directly add much to GDP for the first two decades.
The next false argument is saying ”by the time the 50s babies were moving out, the population was higher so the ratio of new homes needed was not as dire”, as if the infants of the 1970s could provide construction labor