Shared ownership schemes are very good but there aren't very many of them as a share of the overall housing stock.
Prices in areas like FH have shot up so fast in recent years that the ability to own is essentially decoupled from earnings. You can spend years saving only to find prices have gone up by more than the amount you saved.
Wealth is now the principal determinant of the ability to buy around here, usually from existing property or from family subsidy. Another way to describe this is luck.