Horrifyingly easy. All it can take is health problems that mean you can't work or need a housing benefit top up followed by needing to move and 99% of landlords will treat you like a piece of dirt and refuse you point blank. Some LL's will even evict you if you start to claim HB/UC but want to stay and can pay the rent. Nothing good in your past will matter or make a difference, only that you are now benefits scum. Even if you offer to pay upfront and even if you have a guarantor.
This happens even though a blanket ban on benefit tenants has always been discriminatory, and the recent court case ruled it so officially, but the thread about that decision is evidence of the huge prejudice against benefit tenants regardless of their (our) individual circumstances.
Councils can, and do, put up all manner of obstacles against registering as in housing need, even for those who are street homeless, eg a residential link or familial or work link to the area and it is perfectly possible to fall through the cracks as each council tries to accept responsibility for as few claimants as possible because they are so short of housing.
As a couple without children for example, the majority of councils in the UK will restrict you to a 1 bed property only so if there are no 1 beds available then you cannot bid on any property, in addition people who are street homeless will almost always take priority over singles/couples who are sofa surfers, and often elderly downsizers moving to a one bed will take priority of a homeless-sofa surfing couple because the larger property needs to be freed up. It is possible to be awarded the highest level of housing need/points including medical need and still get no higher than 5th or 6th on the list in over 2 years and so are never offered any property that you bid on.
Many council/housing association homes also have restrictions on them that are aimed at keeping a mixture of types of tenants in the area eg working and non-working, and so have additional eligibility requirements. That idea has its advantages, but try being the homeless person who can't work due to health problems and being denied a home as it is for working people only, someone who arguable is in less need than you since they are fit and well enough to work.
Also, if you are granted homeless status, often the only emergency accommodation are hostels for single people which can be miles form your previous address/doctor etc, and even if you have health needs and one of you cares for the other, this will not taken into account at all and so the only option is to be separated if you cannot sofa surf or live in a car, a tent etc.
Many people with MH problems do not want to live with other strangers who may behavioural or MH problems, or alcohol problems as there is so little support there can be a risk of getting caught up in a downward spiral or simply being frightened of living in close proximity with strangers due to their autism, MH issues or past abuse etc So hostel living can be an impossible or a frightening choice and that leaves the street, a car etc.
It is very bad for people with children too obviously but having children in need means that councils can find it more difficult to do absolutely nothing for you. It can be easier to be allocated a hotel room or bedsit than for people without children. And that's a good thing of course, but terrible if you are the one without children.
The point being that more people need to be aware that it isn't simply lack of money that causes homelessness, so having 3 or 6 months savings won't always save you.
It is a structural/bureaucratic/prejudice issue - the money can be claimed so long as you have an address to do it from, if you have friends/ family who will let you do this and its not without its own complications and consequences, and/or can find a property that you can afford from housing benefit/UC that will only pay up to the lowest 30th percentile of the rents in that area ie the cheapest 3 out of ten rents (and this has only just gone up from the 10th percentile, which made/makes some areas completely unaffordable depending on the variation across your local authority area, the cheapest 1 out of ten rents so people can be forced to move across the county with implications for job opportunities, schooling, doctor, family support etc); it is also the housing crisis.
We have a dire lack of council/social housing due to sell offs and population increases and far, far too many LLs holding unconscionable prejudice so people are prevented from having a home even if it could be paid for through benefits.