You could argue mortgages are more affordable due to low interest rates but the counter argument is a deposit is harder to obtain when you get 1% interest on your savings opposed to 5%. So does a low interest actually increase or decrease demand or does it make no real difference?
Tinkering with mortgage (artificial) interest rates, minimum deposits, gazumping rules, etc.. will not reduce homelessness. There is only one way to really change the
housing deficit and that is to make more houses available to those who need it. Yes, simplistic and trite, but that can only be addressed from two directions:
1) increase the housing stock by building more. If there isn't enough profit to interest builders, then local and national government must stop selling their land and build on it themselves. There was nothing wrong with municipal housing per se in the UK until the government decided to bribe sitting tenants in the hope that they might vote for them. The even more critical aspect of that act was to prevent local authorityies from using the proceeds to create more of the same.
2) somehow, (and this is difficult and electorally risky) change the psyche of householders that residential property is an investment rather than a place to live. It would take at least a generation of financial nudges to deter the cynical spiral of rising house prices, multiple home ownership and absentee property ownership.
There is evidence that the bullet is gradually being bitten in the recent announcement about paying for care by placing a charge against property. There was uproar from those who forsee a personal loss because they have gamed the housing market as an investment and would expect their care costs to be paid from public funds in order that their offspring can benefit form their inheritance. I think that as the housing situation gets worse, public opinion may decide that this is not only a fairer way to fund long-term care, but it will also increase the housing stock eventually.