The point of a deposit is to mitigate the bank's risk - who are lending the mortgage - in case the property needs to be repossessed and sold and there are market fluctuations in prices. So if they ask you for 20% deposit, they are effectively ensuring themselves that they can recoup their lending if you fail to pay, even if house prices drop 20%.
This was in response to the financial crisis mainly, that 100%+ mortgages virtually disappeared. Because those mortgages implicitly presumed that house prices would always rise.
The other option would be to do away with desposits but have much more stringent lending criteria, so people needed to earn greater multiples of the amount borrowed and show much more security of income (massively disadvantaging lower earners compared to current setup and also those who are self-employed).
The only other option I could think of would be banks requiring people to take our very comprehensive insurance for job loss/ business failure/ critical illness as well as life insurance when they take out a mortgage. But this would be £££ per month so again put ownership out of reach for many who might otherwise manage it. And even with that there'd still need to be either a deposit or a larger salary multiple to be able to cover the risk of price decreases or interest rate rises that might impact future affordability.
In some countries you can take out a 20 or 30 year fixed rate mortgage. That I think helps people to be able to plan. Often people say "well once you own what does it matter what the house is worth?". Obviously it does, because if you have a 5 year fixed rate and when you come to refinance and the price has dropped, you may well find you cannot refinance affordably at all. Or people get trapped by negative equity, which also harms social mobility in terms of moving for careers etc. Or even to be able to care for family.
These oversimplifications are silly. It is not a simple problem to fix and the UK is not alone in experiencing this.