This is a common complaint and misses the forest for the trees. People say this in NYC all the time too. The reason is because building is banned in so many areas that the few areas where building is not banned see huge amounts of development.
It's the market desperately attempting to meet demand in the face of supply bans but it's not enough. We need to lift the bans everywhere.
The UK is renowned as an incredibly difficult place to build anything, not just housing. It's part of what's strangling your economy - it's impossible to make new things.
It is absolutely not more expensive to live in an apartment than a detached house. Imagine if they replaced the London skyline with detached houses. Would they be more expensive or less expensive to live in? I'm sure we agree detached houses would be more expensive.
On any given piece of land it is always cheaper to have apartments than detached houses. There is no exception to this I have ever seen.
Yet it doesn't work out that way. I don't know why, maybe it's because of the freehold/leasehold system. I mean, look at all the flat-dwellers stuck in flats worth less than their mortgage, paying a huge slice of their income for extra fire-protection because of the cladding scandal (I thank God that was something I was spared).
It costs more to _buy_ a standalone house, but once you own it you aren't stuck having to pay service charges in perpetuity, to avoid the thing falling down or going up in flames (or just because the freeholder wants to make more money out of you and finds new things to charge you for every year).
The big problem with all the council blocks was simply that they were built with little allowance for the cost of maintaining them. Hence councils mostly didn't bother, because they couldn't afford it, and they became undesirable places to live in. Once privatised and sold off to people with high-incomes many of those places became quite desirable, but only for those who could afford to pay those high maintenence costs.
I mean, one would _think_ high blocks would be cheaper, because you fit more dwellings on the same bit of land, but in practice they always seem to turn out to be very expensive to maintain.