I'm still waiting to hear about what investment vehicle the OP recommends that will reliably give me 1/4 to 1/3 of my income for the rest of my life in the way that paying off a mortgage will. Not having to make housing payments in older age is such a massive burden to take out of your old age financial planning.
The OP makes too many assumptions, like that paying off a mortgage and paying rent are roughly similar in upfront cost. The reason why that's not true at the moment is because most private landlords are borrowing money at a higher interest rate that you'd be paying as an owner-occupier, and also trying to get a profit on top of that. If you can get monthly payments at a lower rate than what you'd be paying in rent, then owning is a clear financial win.
Not just London, it's true for large parts of the UK. My mortgage payments are roughly 30% less than what I would be paying if I were to be renting a similar property in my area.As someone else pointed out in London rent is higher then the mortgage costs so I have never understood these arguments (and higher by quite a bit as well)
Edit: just to add some numbers I remember seeing my landlords mortgage statement by accident (honestly) and he was around 800 a month and we were paying 1200 a month. Also that was a reasonable rent price for that area as well!
The OP makes too many assumptions, like that paying off a mortgage and paying rent are roughly similar in upfront cost. The reason why that's not true at the moment is because most private landlords are borrowing money at a higher interest rate that you'd be paying as an owner-occupier, and also trying to get a profit on top of that. If you can get monthly payments at a lower rate than what you'd be paying in rent, then owning is a clear financial win.