With higher rates the average home buyer will simply give less money to the former owner of a property and more to the bank over their lifetime. It will make no difference to overall affordability.
And before anyone harps on about saving for a down payment... consider that we're in the middle of a rental affordability crisis also, with rents rising 10%/yr... Why?
Well, wealthy property investors just shrug off the lack of capital growth going forward and jack up rents to maintain their total returns. Who can blame them?
If i'm a landlord I'm not going to settle for 3-4% rental yields (common in recent years in the South East and London) when I can earn that on risk-free government bonds in a much more tax advantaged way (there is no cap gains tax on them)
Furthermore the truly eye-watteringly wealthy will just buy property at a discount should the nominal price crash actually happen, take advantage of rising yields, and then wait for the next credit cycle to lever up again.
Let's not even get in to the National Debt which will put upward pressure on taxation over the next decade if rates remain high, and the frozen tax thresholds dragging tax payers in to paying more as inflation stays high.
The sad reality in the UK is real inflation adjusted earnings have been flat for decades. My entire adult working life in fact.
Those who think house prices are the problem need to consider that the median house price, adjusted for CPI, is actually the same as in 2007, before the GFC, when rates were also 5% or so...
The variable that changed (or rather didn't change) is salaries
The narrative needs to move to productivity and wages, because the UK is steadily becoming a poorer nation