An increase in long term interest rates will also bring house prices down. That won't make an 80% mortgage more affordable, but it'll make saving for a 20% deposit easier (and will make houses cheaper for people who pay a larger fraction in cash.)

Long term interest rates have been pretty stagnant recently even as the Fed has been raising the short term rate steadily, but they've only just begun winding down their QE assets so if there isn't a recession in the next few years we should see house prices ease off.