Debtors have to make even on their mortgage, at least, so an increase in prices also drags rental rates up - either because the landlord bought later and has higher costs; or because the increase in prices drives up property tax and thus increases costs on existing properties.

If the market worked, you'd see people building multi-family units everywhere until supply caught up with demand, and then you'd see a huge crater in prices as people who took a bath on real estate speculation were overrun with the resulting supply glut. This doesn't happen, for a host of various reasons. Governments want housing to be simultaneously affordable and an investment, which is impossible. Hence most cities wind up building a sort of shadow immigration system, through rent control, selective property tax moratoriums, and so on. People who have lived in a city all their life enjoy lower rents, subsidized by people who just moved in and have to buy at market rate.

A market working does not imply the creation of unlimited supply. Governments that restrict building are an external factor. Markets can only operate within those bounds. Since land for building is scarce, prices rise.

There are other factors, of course. Just speculation does not really seem to be a major one.

Key word here being "working". The market is literally hindered here by said government. The natural response to high demand for housing would be more housing and higher density housing. Zoning laws do a fantastic job of hammering that down.

Renter here. I have yet to find a person who pays a lower mortgage then I pay renting. Renting also goes up every year with little ability of the renter to arrest that increase. In my experience the renter is usually paying the full cost of the mortgage, plus a little to the landlord. The landlord has no savings or interest in improving or fixing anything past the bare minimum.

So why don't you buy? I am in the opposite position. I would like to buy something, but I can not find anything that would be worthwhile (mortgages lower than the rent I pay at the moment, or lower than rent I could ask for renting out).

Not GP but usually the big reason for not buying is that you either need a large amount down (20% in my market, or 10% + additional monthly "Mortgage Insurance" payments until you hit 23% ownership). Average home price in the "Greater Area" around the city (meaning you might still not live close enough to be able to use public transit) is currently ~$665,000 according to Zillow, which means you need to come up with ideally ~$133,000 to put 20% down, or ~$66,000 and pay a premium on top of your mortgage. Either way, this huge down-payment is in addition to the ~7-15k in closing costs you'll be paying. Even then, you're bidding against cash buyers who are willing to waive inspection, so good luck.

$70k-150k up-front isn't easy to save up for even above-average earners (remember, these are average home prices, not luxury homes), so anyone earning average or below is forced into either renting forever, or moving to another town.

Mortgages are generally cheaper than rents right now in the UK, provided you have capital put down for a mortgage

But how much capital? You also have to consider opportunity costs of putting down that capital.

Maybe if I put down one million and borrow another 300k, I can get a low mortgage. But I also lost one million.

Total return on the housing market has kept pace with the stock market in the UK for 20 years so there hasn't been much opportunity cost over here.