Housing supply has recovered somewhat in the past few years but is still low by historical standards. Look at the graph. Notice that the downward trend started from the late 40s began when the Town and Country Planning Act was brought in.
Bear in mind that housing has a natural state of attrition; old houses and flats no longer fit for purpose get pulled down and replaced eventually. So "XX homes built" is not in any way the same as "XX new homes added to the total supply"; a lot of housing is just replacing old housing.
The UK has the world's oldest housing stock, and a lot of it will have to be replaced, so we actually need to be building a lot faster.
Obviously, nobody wants to tear down a gorgeous Georgian townhouse in the middle of Oxford.
But the northern town where I come from has acre after acre of Victorian terraces that were thrown together quickly in the 19th century to house the urbanizing population; they are not well-built (big cracks up the sides due to lack of foundations, which also makes it hard to plant trees nearby because the roots will cause issues), they are freezing cold in winter, you can't insulate them properly without covering the outside with clumsy looking cladding and if you do do that, you often get damp issues, which get even worse if you try to add air con, and we face more heat waves in the future.
These terraced housing streets are too dense to allow off-street parking, but not dense enough to create the sort of ecosystem that allows people to live fulfilling lives without a car, so cars clog the streets and block/wreck the pavements.
A lot of this housing needs replacing too. If you replaced a lot of these streets with a mixture of townhouses (three storey, please, give people a bit of space and a couple of extra rooms!) and medium-sized apartment blocks, you could handle a lot of the housing shortage just like that, AND the residents would have warmer/cooler homes and more floorspace per person.