@RedToothBrush
Example: If we have £50,000 in equity and a 4 bed detached is currently £250,000 and our household income £40,000 that's 5 times our theoretical income
If we lose thirty percent equity we still have £35,000 But the £250000 house becomes £175,000. That's 4.375 times the household income and therefore potentially easier to get a mortgage for that multiple
In theory
You might need to check the maths on this.
I assume that when you say that you have £50,000 equity, you mean that this sum is the difference between your mortgage and the current value of your house - e.g. your house is worth £150k but you've only got a £100k mortgage, giving you a positive equity of £50k. (If you currently have the 'equity' as cash in the bank, then the following does not apply).
You suggest that if house prices fall by 30% you will only lose 30% of your equity. This is incorrect. You lose 30% of the value of the house, which might wipe out your equity completely. E.g. If your current house is worth £150,000 and falls in price by 30%, the new market value is £100,000, and if you owe £100,000 you now have no equity.
If your house is currently worth more than £150,000 then your equity position becomes negative after the price falls - E.g. If you have a £200,000 house and £50,000 equity. The house price falls by 30% to £133,333, but you still owe £150,000 on the mortgage, so your equity is now a negative of £16,666 - you owe more than the house is worth.